Hubbard-to-Heisenberg crossover (and efficient computation) of Drude weights at low temperatures

TL;DR

This paper presents a method to compute low-temperature Drude weights in one-dimensional quantum systems using non-equilibrium dynamics, enabling access to regimes difficult for traditional equilibrium approaches.

Contribution

It introduces a practical approach combining DMRG with non-equilibrium states to efficiently calculate charge and thermal Drude weights at low temperatures, bridging Hubbard and Heisenberg models.

Findings

Thermal Drude weight of the Hubbard model at low T was successfully computed.

Non-equilibrium simulations are less demanding and simpler than linear response methods.

At half filling and low T, thermal transport is dominated by spin excitations.

Abstract

We illustrate how finite-temperature charge and thermal Drude weights of one-dimensional systems can be obtained from the relaxation of initial states featuring global (left-right) gradients in the chemical potential or temperature. The approach is tested for spinless interacting fermions as well as for the Fermi-Hubbard model, and the behaviour in the vicinity of singular points (such as half filling or isotropic chains) is discussed. We present technical details on how to implement the calculation in practice using the density matrix renormalization group and show that the non-equilibrium dynamics is often less demanding to simulate numerically and features simpler finite-time transients than the corresponding linear response current correlators; thus, new parameter regimes can become accessible. As an application, we determine the thermal Drude weight of the Hubbard model for temperatures T which are an order of magnitude smaller than those reached in the equilibrium approach. This allows us to demonstrate that at low T and half filling, thermal transport is successively governed by spin excitations and described quantitatively by the Bethe ansatz Drude weight of the Heisenberg chain.