Correlation functions of an interacting spinless fermion model at finite temperature

TL;DR

This paper develops a method to compute correlation functions for a 1D interacting spinless fermion model at finite temperature, unifying various known limits and providing a comprehensive integral representation.

Contribution

It introduces a novel combination of lattice path integral and algebraic Bethe ansatz techniques to derive a multiple integral formula for the Green's function.

Findings

Reproduces known zero-temperature results

Recovers infinite-temperature behavior

Matches free fermion limit results

Abstract

We formulate correlation functions for a one-dimensional interacting spinless fermion model at finite temperature. By combination of a lattice path integral formulation for thermodynamics with the algebraic Bethe ansatz for fermion systems, the equal-time one-particle Green's function at arbitrary particle density is expressed as a multiple integral form. Our formula reproduces previously known results in the following three limits: the zero-temperature, the infinite-temperature and the free fermion limits.