Imaginary Time Correlations for a High-Density two-dimensional Electron Gas

TL;DR

This paper demonstrates the use of phaseless auxiliary field quantum Monte Carlo to compute imaginary time density-density correlations in a high-density two-dimensional electron gas, enabling analysis of dynamical properties in medium-sized fermionic systems.

Contribution

It introduces a methodology combining quantum Monte Carlo with numerical stabilization techniques to calculate imaginary time correlations for medium-sized 2D electron gases.

Findings

Successful calculation of correlations for up to 42 fermions

Implementation of stabilization techniques for large matrix operations

Assessment of inverse Laplace transform for dynamical properties

Abstract

We evaluate imaginary time density-density correlation functions for a two-dimensional homogeneous electron gas using the phaseless auxiliary field quantum Monte Carlo method. We show that such methodology, once equipped with suitable numerical stabilization techniques necessary to deal with exponentials, products and inversions of large matrices, gives access to the calculation of imaginary time correlation functions for medium-sized systems; we present simulations of a number up to 42 correlated fermions in the continuum, using up to 300 plane waves as basis set elements. We discuss the numerical stabilization techniques and the computational complexity of the methodology. We perform the inverse Laplace transform of the obtained density-density correlation functions, assessing the ability of the phaseless auxiliary field quantum Monte Carlo method to evaluate dynamical properties of many-fermion systems.