Efficient evaluation of partition functions of frustrated and inhomogeneous spin systems

TL;DR

This paper introduces a scalable numerical method for accurately computing partition and correlation functions in complex inhomogeneous spin systems, demonstrated through finite-temperature analysis of 1D bosonic optical lattices.

Contribution

A novel, scalable numerical algorithm for evaluating partition functions and correlations in inhomogeneous 2D classical and 1D quantum spin systems.

Findings

Successfully applied to 1D bosonic optical lattices

Provides controlled error estimates

Enables analysis of finite-temperature properties

Abstract

We present a numerical method to evaluate partition functions and associated correlation functions of inhomogeneous 2--D classical spin systems and 1--D quantum spin systems. The method is scalable and has a controlled error. We illustrate the algorithm by calculating the finite--temperature properties of bosonic particles in 1--D optical lattices, as realized in current experiments.