Dressed excitations, thermodynamics and relaxation in the 1D XXZ Heisenberg model

TL;DR

This paper explores how thermodynamic Bethe Ansatz dressed excitations influence thermodynamics and relaxation in the 1D XXZ Heisenberg model, connecting microscopic excitations to macroscopic physical properties.

Contribution

It provides a detailed analysis of TBA dressed excitations' role in thermodynamics and relaxation, and compares multi-string and single quasi-particle descriptions.

Findings

Temperature-dependent dispersions match known thermodynamic behaviors.

Derived a formulation of Drude weights from finite wavevector relaxation.

Contrasted string excitation and quasi-particle descriptions in low-energy theories.

Abstract

In this note, we discuss the low and high temperature contribution of Thermodynamic Bethe Ansatz (TBA) dressed excitations in the thermodynamics and energy-magnetization relaxation within the Generalized Hydrodynamics approach in the linear response regime. In particular, we show how the temperature dependent dispersions of the excitations reproduce well known behavior of the specific heat, magnetic susceptibility, spin and energy Drude weights. In this context, we derive a further formulation of the Drude weights from the finite wavevector relaxation. Furthermore, we contrast the TBA description of thermodynamics and dynamics in terms of a multitude of string excitations to that in terms of a single quasi-particle in low energy effective theories.