The Drude weight of the spin-1/2 XXZ chain: density matrix renormalization group versus exact diagonalization

TL;DR

This study compares exact diagonalization and time-dependent density-matrix renormalization group methods to analyze the temperature dependence and finite-size effects of the spin Drude weight in the integrable spin-1/2 XXZ chain.

Contribution

It provides extensive low-temperature data for the Drude weight using tDMRG and discusses finite-size scaling and ensemble effects in ED calculations.

Findings

tDMRG achieves lower temperature results for D.

Finite-size effects are analyzed in ED data.

Behavior of D near SU(2) symmetry is discussed.

Abstract

We revisit the problem of the spin Drude weight D of the integrable spin-1/2 XXZ chain using two complementrary approaches, exact diagonalization (ED) and the time-dependent density-matrix renormalization group (tDMRG). We pursue two main goals. First, we present extensive results for the temperature dependence of D. By exploiting time translation invariance within tDMRG, one can extract D for significantly lower temperatures than in previous tDMRG studies. Second, we discuss the numerical quality of the tDMRG data and elaborate on details of the finite-size scaling of the ED results, comparing calculations carried out in the canonical and grand-canonical ensembles. Furthermore, we analyze the behavior of the Drude weight as the point with SU(2)-symmetric exchange is approached and discuss the relative contribution of the Drude weight to the sum rule as a function of temperature.