Non-equilibrium thermal transport and vacuum expansion in the Hubbard model

TL;DR

This paper investigates non-equilibrium thermal transport in the Hubbard model using DMRG, demonstrating that the steady-state energy current can be effectively described by a simple additive relation and exploring vacuum expansion dynamics.

Contribution

It provides the first detailed numerical analysis of thermal transport in the Hubbard chain, confirming the validity of a simple additive relation for steady-state currents and studying vacuum expansion.

Findings

The additive relation for steady-state energy current holds within numerical accuracy.

Violations of the relation are below the finite-time DMRG accuracy.

Initial equilibrium states radiate into non-thermal states such as the vacuum.

Abstract

One of the most straightforward ways to study thermal properties beyond linear response is to monitor the relaxation of an arbitrarily large left-right temperature gradient $T_L-T_R$. In one-dimensional systems which support ballistic thermal transport, the local energy currents $\langle j(t)\rangle$ acquire a non-zero value at long times, and it was recently investigated whether or not this steady state fulfills a simple additive relation $\langle j(t\to\infty)\rangle=f(T_L)-f(T_R)$ in integrable models. In this paper, we probe the non-equilibrium dynamics of the Hubbard chain using density matrix renormalization group (DMRG) numerics. We show that the above form provides an effective description of thermal transport in this model; violations are below the finite-time accuracy of the DMRG. As a second setup, we study how an initially equilibrated system radiates into different non-thermal states (such as the vacuum).