Commuting quantum transfer matrix approach to intrinsic Fermion system: Correlation length of a spinless Fermion model

TL;DR

This paper develops a quantum transfer matrix method for analyzing the correlation length in a spinless Fermion model, providing numerical solutions that align with conformal field theory predictions at low temperatures.

Contribution

It introduces a QTM approach for Fermion systems and derives integral equations to compute correlation lengths at finite temperatures.

Findings

Correlation length computed numerically matches CFT predictions at low T.

Method applicable to arbitrary particle densities.

Provides a framework for analyzing Fermion models at finite temperatures.

Abstract

The quantum transfer matrix (QTM) approach to integrable lattice Fermion systems is presented. As a simple case we treat the spinless Fermion model with repulsive interaction in critical regime. We derive a set of non-linear integral equations which characterize the free energy and the correlation length of $<c_j^{\dagger}c_i>$ for arbitrary particle density at any finite temperatures. The correlation length is determined by solving the integral equations numerically. Especially in low temperature limit this result agrees with the prediction from conformal field theory (CFT) with high accuracy.