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

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 $⟨j(t)⟩$ acquire a non-zero value at long times, and it was recently investigated whether or not this steady state fulfills a simple additive relation $⟨j(t\to \infty )⟩=f(T_L)-f(T_R)$ 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).

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Cited by in corpus (7)

• Finite-temperature transport in one-dimensional quantum lattice models
• Ballistic transport in the one-dimensional Hubbard model: the hydrodynamic approach
• Transport in out-of-equilibrium XXZ chains: non-ballistic behavior and correlation functions
• Higher-Order Hydrodynamics in 1D: a Promising Direction and a Null Result
• Spin crossovers and superdiffusion in the one-dimensional Hubbard model
• Generalized Hydrodynamic approach to charge and energy currents in the one-dimensional Hubbard model
• Generation of spin currents by a temperature gradient in a two-terminal device