Finite temperature dynamical DMRG and the Drude weight of spin-1/2 chains

TL;DR

This paper introduces a practical method using density matrix renormalization group to study finite temperature dynamics in one-dimensional quantum systems, enabling direct calculation of the Drude weight in spin chains.

Contribution

It presents a novel approach to reduce entanglement growth in time-dependent DMRG by evolving auxiliary degrees of freedom with reversed time, allowing efficient analysis of current correlations at finite temperature.

Findings

Drude weight is nonzero in the gapless phase, indicating dissipationless transport.

The method enables direct extraction of the Drude weight at intermediate to high temperatures.

An upper bound to the Drude weight at low temperatures is established via bosonization comparison.

Abstract

We propose an easily implemented approach to study time-dependent correlation functions of one dimensional systems at finite temperature T using the density matrix renormalization group. The entanglement growth inherent to any time-dependent calculation is significantly reduced if the auxiliary degrees of freedom which purify the statistical operator are time evolved with the physical Hamiltonian but reversed time. We exploit this to investigate the long time behavior of current correlation functions of the XXZ spin-1/2 Heisenberg chain. This allows a direct extraction of the Drude weight D at intermediate to large T. We find that D is nonzero -- and thus transport is dissipationless -- everywhere in the gapless phase. At low temperatures we establish an upper bound to D by comparing with bosonization.