The Hubbard chain at finite temperatures: ab initio calculations of Tomonaga-Luttinger liquid properties

TL;DR

This paper introduces a new ab initio method to analyze finite temperature properties of the one-dimensional Hubbard model, revealing detailed thermodynamic behavior and confirming Tomonaga-Luttinger liquid predictions.

Contribution

The authors develop a novel approach using Trotter-Suzuki mapping and quantum transfer matrix analysis to study finite temperature properties of the Hubbard model.

Findings

Calculated specific heat, susceptibilities, and excitation spectra for various parameters.

Confirmed low-temperature scaling behavior consistent with Tomonaga-Luttinger liquid theory.

Connected the analysis with the dressed energy formalism for ground state properties.

Abstract

We present a novel treatment of finite temperature properties of the one-dimensional Hubbard model. Our approach is based on a Trotter-Suzuki mapping utilizing Shastry's classical model and a subsequent investigation of the quantum transfer matrix. We derive non-linear integral equations for three auxiliary functions which have a clear physical interpretation of elementary excitations of spin type and charge excitations in lower and upper Hubbard bands. This allows for a transparent analytical study of certain limiting cases as well as for precise numerical investigations. We present data for the specific heat, magnetic and charge susceptibilities for various particle densities and coupling strengths U. The structure exposed by these curves is discussed in terms of the elementary charge and spin excitations. Special emphasis is placed on the study of the low-temperature behavior within our ab initio approach confirming the scaling predictions by Tomonaga-Luttinger liquid theory. In addition we make contact with the ``dressed energy'' formalism established for the analysis of ground state properties.