Green-Function-Based Monte Carlo Method for Classical Fields Coupled to Fermions

TL;DR

This paper introduces an efficient Monte Carlo method based on Green functions that enables large-scale simulations of classical fields coupled to fermions without truncation errors.

Contribution

It develops a novel O(N) Chebyshev expansion technique for local Green functions, significantly improving simulation size and efficiency for fermion-coupled classical systems.

Findings

Allows simulation of larger systems than previous methods

Reduces computational complexity to linear in system size

Enables more accurate studies of classical-fermion coupled models

Abstract

Microscopic models of classical degrees of freedom coupled to non-interacting fermions occur in many different contexts. Prominent examples from solid state physics are descriptions of colossal magnetoresistance manganites and diluted magnetic semiconductors, or auxiliary field methods for correlated electron systems. Monte Carlo simulations are vital for an understanding of such systems, but notorious for requiring the solution of the fermion problem with each change in the classical field configuration. We present an efficient, truncation-free O(N) method on the basis of Chebyshev expanded local Green functions, which allows us to simulate systems of unprecedented size N.