Order N Monte Carlo Algorithm for Fermion Systems Coupled with Fluctuating Adiabatical Fields

TL;DR

This paper introduces an efficient Monte Carlo algorithm for fermion systems with adiabatic fields, reducing computational complexity from cubic to linear time, enabling large-scale critical phenomena studies.

Contribution

The paper presents a novel Chebyshev polynomial-based expansion method that systematically truncates matrix operations, significantly improving computational efficiency for fermion system simulations.

Findings

CPU time reduced from O(N^3) to O(N)

Enables systematic study of critical phenomena in 3D electronic models

Benchmark results confirm efficiency and scalability

Abstract

An improved algorithm is proposed for Monte Carlo methods to study fermion systems interacting with adiabatical fields. To obtain a weight for each Monte Carlo sample with a fixed configuration of adiabatical fields, a series expansion using Chebyshev polynomials is applied. By introducing truncations of matrix operations in a systematic and controlled way, it is shown that the cpu time is reduced from O(N^3) to O(N) where N is the system size. Benchmark results show that the implementation of the algorithm makes it possible to perform systematic investigations of critical phenomena using system-size scalings even for an electronic model in three dimensions, within a realistic cpu timescale.