Excited state TBA and functional relations in spinless Fermion model

TL;DR

This paper derives excited state thermodynamic Bethe ansatz equations for the spinless Fermion model using the quantum transfer matrix approach, introducing T-functions and their functional relations to compute correlation lengths at finite temperatures.

Contribution

It presents a novel derivation of excited state TBA equations and introduces T- and Y-systems for the spinless Fermion model, enabling accurate numerical computation of correlation lengths.

Findings

Derived a closed set of non-linear integral equations for correlation length.

Numerically solved equations match previous results with high accuracy.

Established functional relations among T- and Y-systems for the model.

Abstract

The excited state thermodynamic Bethe ansatz (TBA) equations for the spinless Fermion model are presented by the quantum transfer matrix (QTM) approach. We introduce a more general family called T-functions and explore functional relations among them (T-system) and their certain combinations (Y-system). {}From their analytical property, we derive a closed set of non-linear integral equations which characterize the correlation length of $<c_j^{\dagger}c_i>$ at any finite temperatures. Solving these equations numerically, we explicitly determine the correlation length, which coincides with earlier results with high accuracy.