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Interview of Philip W. Anderson by P. Coleman, P. Chandra, and S. Sondhi on 2002 March 22,
Niels Bohr Library & Archives, American Institute of Physics,
College Park, MD USA,
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Covers the gradual move from Bell Labs to Princeton, at first part time then full; discusses work on spin glass problem and ramifications for optimization theory and neural networks; reaction to Nobel Prize; return to localization and Gang of Four paper; thoughts on mixed valance problem and heavy electron systems.
We are gathered here today for the fifth of our interviews with Phil Anderson on his career in physics. Today is March 22, 2002; the interviewers are Piers Coleman, Premi Chandra, and Shivaji Sondhi. We will attempt to cover three sets of topics today. The first of these involves Phil’s move from Bell Labs to Princeton; the second is the cluster of work on spin glasses and its extensions to ideas and in other fields; and finally the work on localization that began with the paper of the Gang of Four. So let’s start with the first of these, Phil. What lay behind your move from Bell to Princeton?
Well, it was a combination of a rather large number of motivations. I sometimes refer to whichever motivation is most germane for the point that I am trying to make to different people. One was really quite important. It became clearer and clearer to me that I could have no influence on either American science or British science if I kept moving back and forth between the two, so that I would essentially be a research instrument without having much political or social influence, or having relatively little. Number two was that Mott had retired as Cavendish Professor, and after a little thought I didn’t apply to be Cavendish Professor. I probably would never have made it anyhow because it’s a very English position. Brian Pippard became Cavendish Professor and he had ideas about physics education that I didn’t really like very much. He wanted to reduce fundamental physics and talk about a lot of applied subjects in different little bits of the field. He also brought in a man named Cook who was really primarily just a functionary to manage the Department for him, and so in that sense weakened the experimental effort. So there were several things he did that I didn’t like very much. Then the third thing was that even with these two disadvantages, if we had found the ideal house in Cambridge or in one of the villages around there, which we kind of desultorily looked for, I probably would have moved entirely to England rather than the US. In spite of the fact that even then it was still true that my English academic salary was like the probable error of my American salary. So I moved to Princeton. That was facilitated very much by John Hopfield. I didn’t at the time know that John, (well he didn’t know) that he was off to Caltech, but he certainly was off to biophysics and he already had in his quiet way become quite adamantly unhappy with the physics department at Princeton. Of course he still asked me to come and didn’t tell me what his problems where, but I should have known. For instance, he hired Richard Palmer, but he hired him here only as an instructor because he felt that it was unfair to hire someone as an assistant professor when basically he had no chance at tenure. He apparently had quite a number of unfortunate experiences with trying to get a young tenure theorist in the department here, and of course at the same time the experimental effort here was collapsing, and I didn’t know that when I accepted. But in any case, I was only going to be here half of the year and I was going to be an Assistant Director at Bell Labs, which was happy to have me come back and really take over some serious responsibility for the administration. So for two years after I got back I was Assistant Director of Physics Research with Joe Burton. Joe really is marvelous and he could have done everything, but for some reason he had earned the distrust of our leaders in the higher management, particularly Al Clogston. I think the problem was that Joe was really much smarter than Al Clogston and Al probably felt that. Joe got away with a lot and I helped him get away with a lot also. We worked very well together, but then Joe eventually left and went off to run the American Physical Society which he did for about ten years thereafter, together with Bill Havens; he was Treasurer and Bill Havens was Executive Secretary. And of course the President doesn’t run the APS; the permanent officers run the APS, and the two of them ran it very well.
Was it your initial arrangement that you would continue to be half and half or had you intended?
Yes our initial arrangement was that I would continue to be half and half. I think John must have promised them that I would take on permanent status, but after 1977 that probably wasn’t a problem, which was I think a very unexpected thing for everyone involved. I brought along I think Ali Alpar and Duncan Haldane with me and we had some arguments about whether I was going to have to pay their tuition with my, at that point, non-existent grants, and as far as I know their tuition is the only start-up funds that I actually was provided. Princeton was not a very hospitable place. They found me just week-to-week housing in this place or that. For some time I had a little flat in the housing complex out on Route 206, Stanworth, and for another while I was allowed to use one of the guest rooms at the institute in this barn like place, the basement of which was full of electronics from the old computers. But I had to vacate that completely week to week. I could put nothing of my own in it. Then when I asked them could I really have some kind of permanent housing, the Housing Department was of no use whatsoever. I didn’t realize then you had to get a Dean at least to talk to the Housing Department before they would do anything useful.
I can report from recent experience that the Housing Department is unreconstructed.
Yes, if you have a Dean pushing for you, you probably can get something done, but I didn’t realize that and I went in and they were very unfriendly and so we left. We looked over at Ferris-Thompson and found what we thought was the most acceptable flat in terms of position and so on, and we asked them for that, and they said oh, all of those flats are occupied. We went around and sneaked in the back way and discovered that five out of six of the flats in Ferris-Thompson were unoccupied, confronted them with that and they graciously permitted us to have the flat. So we finally had a place where we could put some stuff down. After that I came here a little more regularly than I had before. But actually I had a lot of business to do at Bell Labs because after Joe left, and eventually Bill Brinkman took over the Physics Research Laboratory. That was about the time that I was made a Consulting Director and for a while sat in and helped evaluate most of the theorists and many of the experimentalists. But then eventually Bruce Hannay retired (as VP) and was replaced with Arno Penzias, and for the first two years of Arno Penzias’ stay, it was my duty once a week to have breakfast with Arno and go on a laboratory visit of some sort or another and help him evaluate all the different research departments, during which I learned a great deal. Incidentally, I learned a lot of economics. I was very admiring of the Economics Department, which it was one of the new management’s decisions to fire lock, stock, and barrel with the breakup of the company, because the management of the AT&T and the Bell Laboratories felt that they knew more about economics than the Economics Department, which as you know turned out not to be the case. They made at least five different mistakes almost right off the bat, two of which I know the economists advised them against. So I didn’t necessarily learn to respect economists but I learned to disrespect bean counters and financial managers.
When did you make the move to Princeton full-time?
In 1984. I actually retired after 35 years of experience at Bell Labs. I was given full retirement pay. And that worked very well. That was when the AT&T was really breaking up. At that point we decided that we would build a house down here, and while the whole process was rather painful for entirely extraneous reasons we did manage to settle in here. It was a very good time to leave Bell Labs, and I had finished with this rather fascinating experience of sitting in with the Vice President and going through the entire research operation. So I got down here and there was a backlog of students. John hadn’t really had very many students and there was a large number in those days that wanted to do condensed matter. John was busy going off to biophysics more and more and he felt that that was too problematical a thing to start a student out in, and so he was eager to off-load all of his future students on to me. Not only did I have Ali Alpar and Richard and then Duncan, (Richard was left over sitting in this instructor position in which John had hired him). John had come to visit us in Cambridge for a year, and during that year he had gotten to know Richard and admired him very much, but nonetheless he felt it was not a safe thing for Richard’s career for him to take an Assistant Professorship. And Dan Stein was one of the new students, Jim Sethna, a whole group of really quite good students came in and asked me in to give them problems. There were some that were not so great. There was one who is long forgotten, Ki Ma, and I hastened him through with a Ph.D. thesis of which I’m not proud. And there are a couple of others. There was one that came in from Rutgers. Rutgers didn’t have enough solid-state theorists so I guess Elihu (Abrahams) off-loaded one of his students on me. He was pretty good. I had students coming out of my ears. Some of them just trained themselves. Gerry Tesauro has become an important neuro- physiologist, but I didn’t teach him anything. He was interested in non-linear mechanics which I knew very little about, and somehow I noticed his name on the management of the big meeting in neurophysiology, the NIPS Meeting, the big skiing meeting of neuroscience, so he must be quite somebody in neuroscience.
Or in skiing.
Or in skiing or both. There were a number of them. Fleischman was one of the early students, and he was very good, but he was a farm boy from Indiana and he disappeared back onto the farm in Indiana and I guess never made much of a mark thereafter, but he wrote a couple of very good thesis papers with me. I’ll think of the others as we go through.
Maybe this would be a good time to ask you a little bit about the evolution of the ideas that ended up in your paper with Thouless and Richard Palmer on spin glasses.
Well, I think I told you a little bit about Sam Edwards and his visiting us on Saturdays during the year he was waiting to occupy the chair. He shortly thereafter became Cavendish Professor, but for quite a long period he was the nominal head of the CMT, Condensed Matter Theory group. During that year he came around and asked for a problem and I gave him this problem with spin glasses and told him that there was a phase transition, and he said, “Well, in my back pocket I have an interesting method for doing such problems,” and that turned out to be the replica method. But before he had the replica method we worked out between us this self-consistency method for determining that at least there was a phase transition. There was a point at which a self-consistent time independent effective field giving a time correlation between two times infinitely far apart, where that could appear self-consistently. This was the basic principal of the original method which then could be extended to the replica method which gives you a full thermodynamics of the phase transition. So we essentially used this as a mean field theory, assuming a very simple short range Hamiltonian, and at the same time David Sherrington, had been Sam Edwards’ student, heard about this and said well a mean field theory means that if you have an infinite range model you can solve the mean field theory exactly. And so he and Scott Kirkpatrick, who was visiting him at the time, introduced the Sherrington/Kirkpatrick Model, which was essentially what we (Edwards) did except making the observation that if you can do a mean field theory, you can do an exact mean field theory in the long range model. Which we all knew; that was not such a very original idea. But the interesting thing is that it turned out to be very complicated, and I think it was Kirkpatrick who pointed out to David that having done this supposedly exact mean field theory of a specific model, the entropy was negative at low temperature. So they said oops, this doesn’t work. And David Sherrington came and visited me; I believe that was that second year when I had a Stanworth apartment and so I was able to put David up for a few days in the Stanworth apartment and he worked with me for a while. Richard got interested in it — what we arrived at was the Thouless-Anderson-Palmer Method. I guess David had visited during this period also, and so he was aware of our problems and we each independently invented one way or another of doing this. It was what Virasoro used later to call a cavity theory. From one point of view it was the old Bethe-Peierls method; from another point of view, the earliest method of that sort was the cavity local field of Onsager. David invented a diagrammatic way, a way in which you could sum up essentially some repeating diagrams which gives exactly the same answer. So we had three essentially independent ways of arriving at it. I’m not sure if Richard had contributed much to the way of arriving at it, but then at the end you got a set of equations which required the solution of a random linear problem. And so Richard began computing this random linear problem to which the TAP method leads you and he began finding some very strange things about that. So we published the TAP method with Richard’s best estimate as to the appropriate ground state energy. But then Kirkpatrick and Richard more or less, somewhat together and somewhat independently, began to realize that this random matrix problem to which it leads is in itself already a very interesting and very difficult problem, and so both of them were essentially doing what later came to be known as simulated annealing to solve this random matrix problem. The random matrix problem is the linear equation. At absolute zero, it is just the problem of the appropriate eigenvalue of the random matrix.
Perhaps I could ask you just to expand on a crucial conceptual point about this paper. In this paper a crucial insert was that you realized that even though it was a mean field model, you had to involve an Onsager reaction term. Could you talk a little bit about how you came to this idea, because that seems to be a crucial point?
Well that is exactly the thing that we did for which we had the three separate routes. I did know that Onsager’s mean field theory had essentially the same structure. I did know the Bethe-Peierls theory, and that the Bethe-Peierls theory was exact on a Cayley tree. And David essentially simultaneously phoned me and said, “Oh look, you can do this by doing the repeating diagrams,” the diagrams of the high temperature series. They can be classified in orders of the range of the interaction, and the only diagrams that can survive at the lowest order in Z or whatever you want, are these double diagrams which can be exactly summed.
Exactly. So that leads essentially to the Bethe-Peierls theory, which as I said, the earliest version that hadn’t been realized back in the ‘30s when it was done, to be Onsager’s local field.
Now you mentioned earlier about how Richard Palmer’s solution of these equations led to a form of simulated annealing. At what stage in your work on spin glasses did you realize that they were conceptual links to all kinds of other problems, particularly in optimization?
The first such conceptual link I think came from Scott, who said in computational complexity theory, this is an instance of the NP complete problems. The problem of finding the lowest energy of a spin glass is equivalent to a problem in computation complexity theory called the matching problem, in which you would divide a graph into two separate pieces with spins up and then spins down, and you want to do so in the least costly way. And this is known to be NP complete, so you are solving an NP problem with this mean field equation and we thought very highly of ourselves solving an NP complete problem exactly, except we weren’t because it turned out that equation to which our solution led was also NP complete, thus essentially the same problem. So that what was suggested was that one way to arrive at this was to start our spin glass off at high temperatures where we knew we really had the exact solution. Then you had an essentially paramagnetic and anneal it past the transition point and expect the solution as we lowered the temperature to eventually arrive at the ground state.
This of course assumes there is a continuous path between the paramagnetic state and ground state.
Yes, but of course there has to be.
In that type of spin glass, yes.
In that type of spin glass. And then Richard discovered that every time he came down he got a different answer, but they converged more or less to very similar energies, so he picked the lowest one and that was our solution. Scott was the person who said but this is now a general method for solving NP difficult complex optimization problems. We can assume that like the spin glass, they have some phase transition, and that we can anneal from where we know the solution is okay. We know we’re traveling between all the possible basins of attraction of ground states and hope that somehow as we go down we are in the basin of attraction of the lowest ground state; and at least we will be in the basin of attraction of some ground state which will be much better than a random solution. This was the genesis of Scott’s idea of the simulated annealing method. Both he and Richard had been busy doing simulated annealing, but Richard did not realize that it was an important problem in computational complexity theory. So right off the bat, we made the link with computational complexity theory. The tie-ins to other things happened. Well first we published the TAP method and then the replica method, and there is a paper actually that David Thouless wrote in which he said the problem with the replica method is that you are assuming that all the replicas lead to the same solution, but what really happens is breaking of replica symmetry; you don’t use the same value of Q for every replica. He introduced the idea of replica symmetry breaking. And then that led Giorgio Parisi to actually solve the replica symmetry breaking problem with this very ingenious method of having a distribution function of Q’s, which I could reproduce if I had a couple of days, but I can't reproduce off the top my head. It is very ingenious. Virasoro showed in later work that it is essentially another way of making a remark that as you anneal down in the spin glass, starting from some random arbitrary configuration that you have at high temperature, as you lower the temperature you will settle down into the basin of attraction of a particular ground state, but the different ground states have different energies, are different eigenvalues. There are different solutions of the matching problem or the spin glass problem, different ground states of spin glass. And they are not available from each other unless you flip very large numbers of spins, so that for the infinite-range Sherrington-Kirkpatrick spin glass this definitely is the structure. It’s a set of discrete ground states, only one of which is the true ground state, but which accumulate at an energy which is the replica theory ground state energy. And that indeed is in a sense the solution of an NP complete problem if you do this for a specific spin glass. But it is not really a solution of the NP complete problem because it only gives you this energy to order 1/N, the order of the size of the sample and there are differences between the ground states to lower orders, so that the computer scientist who wants the exact solution, doesn’t want an approximate cost only defined to order N; he wants the exact cost. So then there is no contradiction with computer complexity theory. On the other hand, we do much better with the replica exact solution than one does with various computational algorithms that other people have invented. That was where I got back into complexity theory because I said, “Well, let’s take some well- known computer complexity problem.” We chose the graph partitioning problem rather than the matching problem, and , because that’s a problem that many people have invented algorithms for, so there is a compilation of all the solutions and the best solution so far is by some guy named Bui. Let’s see what the replicas give us, and they gave us a better solution than Bui had. So in fact, Yiao-Tian Fu and I (Yiao-Tian Fu was one of the CUSPIA students who showed up somewhat later) so Yiao-Tian Fu and I did the first study of a serious computational complexity problem using the replica method. Fu only got the very simplest case, and it turned out that in any really interesting case it required a great deal more mathematics, and I had very good student named Liao (Wuwell Liao) who actually solved the really hard cases of the same problem and then went off to work with Mike Cross. He and Mike Cross didn’t get on and I think he is somewhere in Silicon Valley. He was a CUSPIA student also, I think. John Hopfield had worked with us a little bit back when he visited me in Cambridge, and he actually was present; he didn’t leave Princeton until two or three years after I arrived. So he was with us at the time when Richard Palmer and I were working on spin glass, so he was very familiar with spin glass ideas and was interested in it all. He went off to Caltech when Goldberger was hired as President of Caltech, and the first gift he gave to Caltech was John Hopfield, because he and John had always been fairly close. In fact it was John’s pressure on Murph (Goldberger) that got me hired here because Murph had been the department chairman, and then Murph, as soon as he knew of John’s unhappiness with practices of the department here, knew he would be an easily recruited individual so long as you didn’t make him live in the Physics Department. So he found a special niche for him in a combination of biology and chemistry, and John has never been within sight of that Physics Department since that time. He really left Princeton in disgust at the practices of the Princeton Physics Department. But anyhow, he knew about spin glasses and learned something about the problem of neural nets, he said, the spin glass is a neural net — the process of cooling a spin glass down is the same as the process of solving a neural net with a certain set of weights. The exchange between the different synapses are the weights or synapses between the different neurons. Then if you would just think them symmetrical and you make the thing have a free energy, then it is exactly a spin glass. And how could I make this spin glass remember things? I don’t know whether he borrowed it from the Mattis spin glass model which is the trivial spin glass that it automatically solves, or he realized that by plugging in a particular pattern of spin configurations via the equivalent of the Mattis Model, he could make the spin glass automatically anneal to that model and that would show that the brain would automatically anneal to any particular configuration that you pumped into it. So he developed what he called a content addressable memory. John being rather a direct person he simply built it into his computer and tested and so he found out how many memories he could simultaneously remember, discovered that it’s about a third the information theoretic limit, which is still an enormous number — it’s still order N memories for an N2 synapses neural net, and that’s the surprise. It really succeeds in remembering very close to the information theory limit. You see, you are setting N squared over two values of the exchange integral. The amount of information in M configurations is M times N, and it turns out that you can get up to M ‘ N over 3, N2 over two bits of memory or N2over three bits of memory and N synapses over two synopsis, which is pretty spectacular. So it was a great discovery. Then what happened was that people said, “Ah, neural nets are non-trivial after all.” Papert and Minsky had insisted that neural nets were a totally idiotic trivial idea, but it is now discovered that neural nets were not a trivial idea and you could do even better with neural nets if you used asymmetric synapses, which is what the brain does, instead of symmetric synapses. So the neural net business went off on its own using what’s called backprop, which is just a spin glass with asymmetric synapses instead of symmetric ones. So John merely re-stimulated all the work that had been done. Still it was a very important role that he played, somehow making people look back. They were looking back anyhow. The guy at San Diego, Rudenberg, he and Terry Sejnowski and a few others were beginning to re-examine neural nets and to use the back propagation algorithm, and John contributed a great deal to that.
Now Phil, your original work on spin glasses was very much motivated by experiment. But then of course you went into all kinds of directions very far away from the magnetic materials that originally inspired it. What were your feelings about some of the developments in the mid ‘80s and also the ‘90s where people actually tried to bring some phenomenological models back to describe for example aging and history dependence in spin glasses using for example these droplet models or something like that?
Well I’m all for it, I think it’s great to come back to the spin glass. You know, here is this experimental NP complete problem for this experimental model for some kind of complex network, and yes you can learn a lot by going back and studying the experiments, a lot of stuff. After all, a spin-flip time can be decreased down to 10-11, 10-12 seconds. That means in one second of a spin glass you have annealed for 1012hops, so with spin glass you learn things with very much larger systems. Well brains are pretty big too, but the actual neural nets that you can really construct on a computer are not.
I wanted to bring up one more thing before we leave the topic of spin glasses. As you know there is been a continuing controversy around people who actually study short range spin glasses on whether the Parisi Solution with all of its complicated structure is in fact germane to the actual solution, in particular the work of Fisher and our own colleague David Huse suggesting ultimately the only symmetry breaking that takes place is that of an Ising symmetry for a short-range Ising spin glass. Do you have any thoughts on the significance of such claims, which of course remain contested?
Some such claim must be true, because although I have never persuaded a graduate student or post-doc to think about the problem, there is a connection between information theory and spin glass ground states, how could you specify, if you have a short range spin glass, you have only order N numbers that you are specifying, and how could you specify more than one or a finite number of ground states if you have only N bits to specify it with. Information theory tells you that something like Fisher-Huse must be true for short-range spin glasses. Now what is amazing is that nonetheless the replica theory gives you approximate answers for short range spin glasses, but it must be simply a matter of coincidence and a matter that mean field theory works better than it has any right to, but it can't be exact and it can't be really rigorous in any sense simply because of this information theory observation. Though if you are interested in one of these imaginary networks, one of these various kinds of complex optimization problems or neural net, you don’t have this restriction of that to having a geometry; so that the brain specifically has lots of small world connections that make it into a “small world” you can get from one place to another with a few — e. g. six — synapses anywhere in the brain. So these long range connections, interestingly we were thinking about long range connections back when we were doing it. But basically it’s a theory which is exact on a Cayley tree except that the far part of a Cayley tree is weakly connected back to the origin of the tree, and that is the condition for the Sherrington-Kirkpatrick-Anderson-Edwards method really to work. So yes Fisher is nominally correct, but the interesting problems are not problems exactly modeling reality, well, two things: one is real spin glasses seem to obey mean field theory remarkably well; and the other is where you really understood in using the spin glass that there is no such restriction, usually it’s been a small world network connecting it. Who’s to tell you what the connections are in the random network that represents the interactions between different parts of the genome, for instance, which is a third or a fourth use of spin glass-like Hamiltonians to model rugged landscapes for evolution. The landscape in has no geometry as far as you know, it’s just whatever works, and you don’t know whether those interactions are short ranged or long ranged, but you are pretty certain that they are long range. So if you want to model evolution you might as well use those long range spin glasses, and of course this is true for the brain, as I said. There are still other applications of spin glasses, of this kind of approach. Nick Sourlas has used the spin glass as or maybe only the random field model as a way of constructing error-correcting codes, for instance. It’s gotten into all kinds of nooks and crannies that you wouldn’t expect it to be. But the rugged landscape is very interesting, and there is no reason why interaction should have a geometry . Glass is another. Well there is a model for glass that doesn’t resemble a piece of a silicon compound; it’s the multi-spin interacting spin glass that does seem to reduce to the dynamic equations of a true glass. That’s work that Mezard and Parisi and others have been doing, again generalizing TAP and the replica method to a new direction and maybe having a useful model for glass. So spin glass itself, whether or not it is really an efficient use is not too important a question.
Maybe it is a good point to take you in a new direction and turn back to 1977. I would like to ask you the question how did you react, and in particular how did you manage to keep going and remaining an active researcher after you received the Nobel Prize?
Well a couple of things. Let me mention a little bit of history. Actually the real surprise was when I got the so-called Dannie Heinemann Award from the Gottingen Academy of Sciences. That was in ‘75, and I thought that I had done a lot of important stuff, but people were just going to forget about localization, and so I was surprised and remarkably pleased when that happened. That certainly was a great motivation to start thinking about localization again. If you read the acceptance speech for that you will realize that I basically hadn’t done anything very much. I wasn’t even on board with the stuff that Mott and Thouless had been thinking about on the connection between localization and conductivity. I was describing my original work. Then in ‘77, to my great surprise, and it really was a surprise, the Nobel Prize. I told you earlier that someone had given me some hints back in ‘73, but then I assumed that was about the Josephson affect and that was over, so I was completely unprepared for the Nobel Prize. The Nobel Prize is a wonderful experience, there is no question that it is a wonderful experience, and everyone should have it. I guess it’s more than 15 minutes of fame, let’s put it that way. I just was meeting this winter with 172 other Nobel Prize Winners, and you would be surprised how few of them just stopped at the time that they got their Nobel Prize. A lot of them switched fields to do something new, and sometimes that is successful and sometimes it isn’t. But then you can name names that don’t ever do anything again and just use the Nobel Prize. You could name people who use the Nobel Prize as a stepping stone to some administrative or useful job; you could name names who switch fields and don’t succeed; and then a lot of them switch fields and do succeed and do very, very interesting things for the rest of their lives. But a lot of them stay in the field and do very interesting things for the rest of their lives. But the exception is to just quit at the Nobel Prize. That is not a danger. Now one thing that everyone who has any sense recognizes, and in fact people talk it over among themselves, everyone knows that the odds on getting another one are zero, that if you have to do it, there has to be some incredible coincidence that happens, like Bardeen doing work with two different sets of collaborators both of whom deserved the Nobel Prize themselves, and so it would have been silly not to have put Bardeen in among the second set of collaborators. So there is no way that you can maneuver yourself into a second one. You don’t even really want to after you have been around for a while. But there is a tremendous motivation you realize there are things you can do, there are influences you can have or you can go on doing your own work. My first thought was, “Great, I’ll never have to retire and I can go on doing condensed matter physics if I want to the rest of my life.” It isn’t hard. Perhaps the temptation to jump into a new field is very high. I did some of that. I am very glad I did some of that, and some of it was quite successful, though not well known. But mostly I stayed in the same field and just went on working because there was lots more to do.
Perhaps you could tell us about the lead up to the Gang of Four paper?
It began with Don Licciardello who came and worked with me. He was my first Assistant Professor. I didn’t have sense enough to rehire Richard Palmer as an Assistant Professor — I didn’t know I was going to get the Nobel Prize, and I think after the Nobel Prize I might have been able to bully the Department into tenuring him, if he did good work and of course he did continue to do great work. Instead they said I could have an Assistant Professor and I hired Don Licciardello. Don came from Thouless’ work on thinking about scaling, the definition of localization in terms of conductivity and the idea of the Mott-Joffe-Regel conductivity. I went around giving talks about localization, and realized that there was all of this old data on films which demonstrated that localization really did happen in the two dimensional metals at the conductance that was predicted by the Mott-Regel criteria or by Thouless, so I got to calling it the Thouless conductances, e2over h in two dimensions. There are these 1917 measurements by the guy who later became the President of the Batelle Institute in Philadelphia, but he was doing a post-doc in England at the same time as the war was going on and there was no coal available, and so he had measurements of the variation of conductivity of bismuth thin films for which the thickness was measured in terms of the deposition time, evaporation time, and temperatures were room temperature but I looked up and the temperature was 17 degrees Celsius because it was wartime in England. But he had these bismuth films, and they would go right up to the minimum metallic conductivity and then they became insulating. So I became a firm believer in the minimum metallic conductivity, which of course Mott was very adamant about — there was a minimum metallic conductivity and you damn well didn’t get below it. So Wegner came around and he had this field theoretic way of doing localization and I remember arguing with him after his talk at length and saying, “But the minimum metallic conductivity, how could there possibly not be a minimum metallic conductivity?” And I had some vague ideas about the scaling in two dimensions.
And this would be in ‘70 what?
That was in ‘77, thereabouts. And then I was lecturing about it, as I remember. as part of my advanced course and was lecturing about scaling, and in the middle of the lecture I suddenly had the idea well you could scale it this way, this is one limit of scaling, so I drew this scaling chart. At lunch the same day I talked to Elihu and Rama, and Rama said, “I kind of remember some of these old results about crossed diagrams diverging done by Langer and somebody,” and he looked them up and he found this diagrammatic theory, and we hooked the diagrammatic theory onto my high-conductivity limit, my classical limit, and we realized there was a beta function that we could construct, one parameter scaling. The localized side was exponentially localized and that gives you a scaling curve too. And so we fitted it all together and drew those curves in a very few days, as a matter of fact.
How strongly had your participation — this is shortly after the ill-condensed matter summer school in Les Houches. I was curious to know whether that school had any influence in your thinking, as far as you know?
Well, in the previous tape I told you the wrong answer to that. In fact it had a lot of influence because I listened to David Thouless’ lectures, and I think that whether I understood about conductivity and its relation to localization before that, I certainly understood about it after that. Considerations of dimensionality and so on. It was the next year, in ‘78, after coming back from that summer school that I was doing advanced condense matter lectures, and Rama Ramakrishnan was here and Don Licciardello. Don Licciardello’s place was to do some rough numerical estimates that showed that we were more or less on the right track. So the Gang of Four was a consequence of my going to [Les Houches] in the summer of ‘78 and Ramakrishan’s being here with that very useful suggestion about the diagrams which later became the weak localization diagrams. At about the same time, I was still going to Bell Labs of course, and about the time we had this idea, Doug Osheroff came to me with some curves. He had been measuring low temperature conductivity, I don’t know for what or why. I guess he was looking for the minimum metallic conductivity, he didn’t see anything of the sort. He had this curve, and something which Doug would do but very few other people would do, he tilted the paper up and sighted along it and he saw that it wasn’t straight, that he was doing I versus V and not getting a straight line. I took a look at it and I said, “Oh, that’s an xlogx, so that if you plotted the conductivity it would be logarithmic. And I said, “But that’s what we’ve just been deducing and we got some logs from the theory of localization. Maybe you were seeing our log.” And he was, and so he and Jerry Dolan I guess published the first paper showing weak localization in these thin films. They were nasty dirty thin films of mixed gold and bismuth or something like that. Later on he did two dimensional resistivity in MOSFETS, and eventually there is a beautiful sequence of work by Bob Dynes in which they really checked out weak localization theory. But the first measurement of weak localization per se was done by Doug Osheroff, and it’s fortunate that Doug is a very careful experimentalist and he doesn’t believe that a straight line is straight unless he lines it up.
How was the scaling theory received by the community? Was there skepticism there?
No, the minute there were those logarithms I think the community bought it hook, line, and sinker, and I’m not sure they should have — I’m not sure it was really all that great. But in fact we did prove out that there was that logarithmic term in a number of different cases. Then when other people generalized to spin orbit coupling and so on, so you could see the little singularity at low temperatures and the singularity in magnetic field, the localization theory became a very much received wisdom, altogether too much. Because actually I never really believed it completely. Well not believed it, but I always had this speculation, this question in the back of mind about how the diagrammatic theory, however you derived it, whether you used Wegner’s field theory methods or our direct diagrammatic method or whatever, it’s still a statement about averages and I was fairly certain that the problem of the conductivity was not self-averaging, not perfectly self-averaging at least. That became — Well, way back in the early days of localization there had been this paper of Lloyd’s in which he proved conclusively that a density of states which was Lorentzian couldn’t possibly be localized, and it turned out he was wrong because he was looking at the average Green’s function instead of the typical Green’s function, and yes you can get rid of that by looking at two particle Green’s function which was a product of one particle Green’s functions. And to my mind there is still no particular reason why the average two particle Green’s function should represent a real average, because the real thing is the sample that you have in front of you; it’s not an average one, it’s a typical one. So I was always unhappy with this question of how good was this wonderful scaling theory. So I think I was the biggest skeptic of this scaling theory all along.
The publication of this paper lead to a tremendous flurry of activity in the Soviet Union. Can you talk about how that developed. Did you have actually direct interaction with the people there?
This was a period when Aspen, well there was one year when Aspen had eight Soviet theorists. That was before the thaw really began, but somehow we wangled or David Thouless and Elihu Abrahams wangled the visit of eight Soviet theorists. Migdal(?) was there, and Gor’kov. You know that caricature of me by Gor’kov dates from that year. And some others, Alexei Abrikosov bowed out because of his fiddle-faddling with Annie Nozieres. But they were real Landau school people except for one guy who was nicest and smoothest of them all; he was a Georgian but he was obviously the commissar that was supposed to take care of them all. I think Elihu had much closer contact with the Russians. He went actually to that Lake Ban summer school, and Patrick I guess went to that. But Elihu was involved with the negotiations, Elihu and Peter Wolff were involved with the negotiations to get us back in contact with Russian theoretical physics. But I think in fact didn’t Patrick actually write a paper with Larkin?
So I think the contact was made by them. I didn’t — in the first place I had been to Russia; I think I have the tendency to go to a place only once, I don’t know why. Well I don’t travel, even then I wasn’t traveling terribly easily. There was a long period when I was more or less boycotting Russia because of the misbehavior and the Sakharov business and so on. But that was probably after my explicit boycott, but I just didn’t get back. So it was really Elihu and Patrick that transmitted the word about localization. This problem is it really self-averaging eventually resulted in a paper. This is the second Gang of Four the Thouless, Abrahams, and Fisher paper, a new method for a scaling theory. And really the most important paper is “New Method II” which appeared in 1981 that was by me alone, and that essentially contains the essence of a way of doing the universal conductance fluctuations, which of course are the indication that conductivity isn’t self-averaging. So I think other people were doing very similar things. I don’t know whether Stone and Lee had really started out on the universal conductance fluctuations first, but basically if you read “New Method II” you will find it has — Actually Az’bel was the first one to make the statement that the conductance has enormous fluctuations. And it’s hidden away somewhere in Thouless’ work in that he shows that the average sigma and the average one over sigma are not the same; they don’t average, they don’t give you the same number. But this was the method that made me happy to show that it was not self-averaging, and that then field theory in fact doesn’t tell you the whole story.
Phil, I would like to ask you about some of your thoughts towards the end of your very active period of work on localization, in particular the paper you wrote with Hans Engquist about definition and measurement of electrical and thermal resistances in 1981. Could you tell us about that?
Well, poor Hans. I’m not sure I should say too much about him. But he was the post-doc whom I designated to work on these ideas which were questions about exactly how do you define resistors when you get down to the scale where you are looking at localization effects. There is no particular reason why the voltage along a wire which is considered to have a quantum fluctuation, why the voltage should be falling uniformly, and so the question is how do you define resistance, how do you define conductance. Mark Az’bel was insisting on one particular solution of that question, and I guess Landauer was insisting on some definite solutions and this was to some extent a continuing argument with Landauer which was mostly off the record, because in the end Landauer turned out to be more or less right. But with Hans what I was doing was trying to think how would you define voltage, and how would you make a voltmeter as a quantum object in a quantum resistor where you don’t have thermal equilibrium. Again it’s this question of on the quantum scale things are not really self-averaging, and so you want to define resistance, or define capacitance, for instance, in order to make a quantum object which is a capacitor. So this isn’t the first, by any means, paper about mesoscopics because I think perhaps Landauer probably has, but this is one of the first papers about what is now known to be mesoscopics in consideration of when you get down to the scale where thermal equilibration is important relative to quantum fluctuations. Then how do you exactly define these various quantities? I am not proud of the paper; I think Landauer has probably kept his head straighter about these things. But at least we were asking those questions at that time. There is one other thing about localization, which is the question of localization and interactions, the two papers with Fleishman that was what Fleishman was supposed to do, there is the one with marginal fluctuations in a Bose glass where we were trying to explain that a Bose liquid would either be completely localized or would be superfluid. That’s because of the interactions, the fluctuations in potential would be screened out, would be self-screened, and in the end you will have a constant potential in which you would then have a moving Bose gas. And there was one called “Interactions and Anderson Transition” which was our attempt, incorrect, but interesting to do a Fermi liquid theory of localizing systems. So that is the theory paper which is what really probably doesn’t happen when interactions and localization. I mean if interactions didn’t cause any really serious problems, we pointed out that there is a way to think of it as...
Disordered Fermi [???.]
Localized quasiparticles. But of course Efros and Schlovsky already had discovered the Coulomb hole and that kind of thing, so it is rather irrelevant, so that is the end of localization.
Thank you. Before we bring this interview to an end I wanted to ask you a little bit about another area in which you had a lot of influence in the early ‘80s and perhaps the late 70’s dating back to your participation in Ron Parks’ conference on Intermediate Valance, and taking you though perhaps to the first discoveries of super-conductivity in heavy electron systems. Could you tell us a bit about your involvement with this field, and I guess taking you from the early stages of the Rochester Conference?
The Rochester Conference, I wrote the summary paper for that conference. I really was pretty much an observer. I had various points, some idea that I had but I couldn’t solve the problem. I don’t think I made much progress with it. I think Maurice Rice was making more progress with than I was, over the years in particular. In so far as you can consider a dilute electron material, of course that’s the Kondo problem, and I was interested in it because of the Kondo problem because essentially I could see that what was happening was the Kondo renormalization. The main work actually, the most important work possibly, was what Duncan was doing. Duncan was doing this paper on the interaction of boson degrees of freedom with the Kondo renormalization. We were kind of aiming at the Kondo volume collapse. But mostly I was just following and advising, talking to all kind of experimentalists, and very much interested in this question of what the heck was going on. Started way, way back in 1970 when Ted Geballe first looked at samarium hexaboride and he saw the first heavy electron phenomenon, although actually what he was seeing was a heavy electron insulator, a Kondo insulator instead of a Kondo metal. But he had these enormous values of specific heat and enormous values of various constants which indicate density of states. Then we were looking at samarium hexaboride at Bell, Jayaraman work on the explosive phase transition in samarium sulfide, samarium chalcogenides. And there I was kind of trying to sort it out into something happening like in samarium hexaboride, a continuous, and then also a volume interaction with a volume degree of freedom and a Kondo degree of freedom which would switch the thing over entirely out of the Kondo mode, in other words there would be a samarium double plus sulfur double minus which would have the samarium ion doing a Kondo renormalization, and then there would be the other phase in the metallic phase where samarium was really truly mixed valence and had undergone a kind of Kondo volume singularity. So it was very important to understand the interaction of bosons with this problem, and also to look at the asymmetric magnetic impurity problem, and that was what Duncan worked on I think while he was visiting here as a student, and then came to Aspen a couple of times while he was working with Nozieres. But he wrote this absolutely wonderful paper about the asymmetric Anderson model which he showed just by thinking hard about perturbation theory you could see how the renormalization paths worked. Which is still about as much as is known about these materials in any really deep sense. Except there is Maurice Rice’s considerations about two things, the TJ Model and his considerations about the entropy that eventually led me to believe that what was happening here was the heavy electrons serving as the free electron gas background for themselves. Essentially it’s more or less like a pretty good precursor of the present day dynamic mean field theory. I was groping towards dynamic mean field theory but I didn’t get there by any means. So my thoughts were dynamic mean field theory but I never really expressed it properly. The only thing I was sure of was that as we find in dynamic mean field theory the famous Nozieres exhaustion phenomena doesn’t happen, and I tried to say that as often and as loudly as possible, that exhaustion wouldn’t happen because the Kondo effect is local in space and there’s only time dependence of the Green’s functions, not space dependence, not a long tail space dependence. So in the course of various talks I gave I kept trying to say some of these things. And of course then you were doing the Kondo resonance.
Where did your curious idea about a large N expansion come from? Was it from talking with field theorists here at Princeton or [???]
No, I just knew they were doing large N expansions. Well, it’s obvious if you have a f function peak which in principle has 14 sub-states, and you only have one electron, that one electron is sitting in the edge and unquestionably the Fermi level is in the edge of your resonance. And the larger N is, the more your Fermi level is on the edge of the resonance. And I think this large N expansion is right for the true mixed valence case; I don’t think it’s right for the Kondo resonance necessarily, but for the true mixed valence cases it works.
Perhaps just to end and to link with what we’ll talk about next time.
And you then took off with the Kondo resonance, which until we got to the modern period of dynamic mean field theory. I think your Kondo resonance was the interim theory between those big ideas of mine and the present day DMFT. I wish the hell I had thought of DMFT, but I didn’t.
Somehow the elements of it were already there in TAP, curiously enough. Just to end, what were your reactions to the discovery of heavy electron superconductivity, which I suppose became evident in 1983 and lead you to write a paper speculating it was P wave pairing?
I was bewildered. I was right, but now I know much more about that, and I’m sure there are higher and higher kinds of pairing. Because it’s simply the same as high Tc; the fundamental interaction is unquestionably a repulsion, and so how could you have S waves there? Why I didn’t say that louder and clearer at the time I don’t know. But in fact they must be, and they are all turning out to be, as a matter of fact. Although it’s rather surprising there are some D and some P.
Well I think there we will end this session.