The Truncated Polynomial Expansion Monte Carlo Method for Fermion Systems Coupled to Classical Fields: A Model Independent Implementation

TL;DR

This paper introduces a software library implementing the polynomial expansion method (PEM) and its truncated version (TPEM) for efficiently calculating the density of states in fermion systems coupled to classical fields, replacing costly diagonalization.

Contribution

It provides a model-independent, efficient computational tool for fermion systems, extending PEM/TPEM applications to new models like the double exchange and diluted spin-fermion models.

Findings

TPEM achieves O(N) computational complexity, significantly faster than traditional methods.

The library successfully applies to complex models such as the double exchange model.

Demonstrates the method's effectiveness in diverse fermion-classical field systems.

Abstract

A software library is presented for the polynomial expansion method (PEM) of the density of states (DOS) developed by two of the authors (N.F. and Y. M.). The library provides all necessary functions for the use of the PEM and its truncated version (TPEM) in a model independent way. The PEM/TPEM replaces the exact diagonalization of the one electron sector in models for fermions coupled to classical fields. The computational cost of the algorithm is O(N) -- with N the number of lattice sites -- for the TPEM which should be contrasted with the computational cost of the diagonalization technique that scales as O(N^4). The method is applied for the first time to a double exchange model with finite Hund coupling and also to diluted spin-fermion models.