Method to correct finite-size effects in many electron systems

A Monte Carlo method is used to calculate the properties of many-electron systems. However, these simulations are only feasible for small systems with a finite number of electrons. In real world applications, systems are often macroscopic. So, finding a way to correct the finite-size effects in simulations is essential.

Dornheim and Vorberger present an innovative formulation to correct finite-size effects in electronic structures.

“The final goal is the description of a macroscopic electronic system in the thermodynamic limit,” said Tobias Dornheim. “While analytical models like the random phase approximation can readily describe the system on large length scales, they generally miss the intricate short-range correlations between electrons that are located close to each other.”

The researchers identified a short-range exchange correlation property that can be estimated from a Monte Carlo simulation with just a few electrons. This can be combined with analytical models to yield the full description of a system. Most surprisingly, the correction displayed an “amazing” performance for systems at extreme densities and temperatures.

“While previous finite-size corrections were only available for different energies, our new scheme goes one step further and is capable of giving a wavenumber resolved finite-size correction of the static structure factor,” Dornheim said.

Dornheim said they have plans to continue their work “along multiple directions.”

“We aim to extend the finite-size correction scheme for the uniform electron gas to the poorly understood regime of moderate temperatures and extreme densities,” he said. “In addition, we will adapt the idea towards more complicated systems, such as hydrogen.”

Source: “Overcoming finite-size effects in electronic structure simulations at extreme conditions,” by Tobias Dornheim and Jan Vorberger, Journal of Chemical Physics (2021). The article can be accessed at https://doi.org/10.1063/5.0045634 .