Energy-twisted boundary condition and response in one-dimensional quantum many-body systems

TL;DR

This paper introduces an energy-twisted boundary condition formalism for thermal transport in 1D quantum systems, providing new insights into thermal response and related deformations.

Contribution

It develops an energy-twisted boundary condition framework for thermal transport, connecting boundary responses to bulk deformations like the boost deformation in integrable models.

Findings

Derived thermal Meissner stiffness for various models

Solved the boost deformation of free fermion chains explicitly

Analyzed nonlinear thermal Drude weights in the XXZ model

Abstract

Thermal transport in condensed matter systems is traditionally formulated as a response to a background gravitational field. In this work, we seek a twisted-boundary-condition formalism for thermal transport in analogy to the $U(1)$ twisted boundary condition for electrical transport. Specifically, using the transfer matrix formalism, we introduce what we call the energy-twisted boundary condition, and study the response of the system to the boundary condition. As specific examples, we obtain the thermal Meissner stiffness of (1+1)-dimensional CFT, the Ising model, and disordered fermion models. We also identify the boost deformation of integrable systems as a bulk counterpart of the energy-twisted boundary condition. We show that the boost deformation of the free fermion chain can be solved explicitly by solving the inviscid Burgers equation. We also discuss the boost deformation of the XXZ model, and its nonlinear thermal Drude weights, by studying the boost-deformed Bethe ansatz equations.