Spin and energy currents in integrable and nonintegrable spin-1/2 chains: A typicality approach to real-time autocorrelations

TL;DR

This paper employs a typicality-based numerical approach to study real-time spin and energy current autocorrelations in one-dimensional integrable and nonintegrable spin-1/2 chains at finite temperatures, revealing key transport properties.

Contribution

It introduces a typicality approach for simulating real-time dynamics in large quantum spin chains, enabling analysis beyond traditional exact diagonalization limits.

Findings

High-temperature spin Drude weight vanishes at the isotropic point.

Typicality holds in finite systems across a wide temperature range.

Full relaxation curves for energy currents are obtained in nonintegrable models.

Abstract

We use the concept of typicality to study the real-time dynamics of spin and energy currents in spin-1/2 models in one dimension and at nonzero temperatures. These chains are the integrable XXZ chain and a nonintegrable modification due to the presence of a staggered magnetic field oriented in z direction. In the framework of linear response theory, we numerically calculate autocorrelation functions by propagating a single pure state, drawn at random as a typical representative of the full statistical ensemble. By comparing to small-system data from exact diagonalization (ED) and existing short-time data from time-dependent density matrix renormalization group (tDMRG), we show that typicality is satisfied in finite systems over a wide range of temperature and is fulfilled in both, integrable and nonintegrable systems. For the integrable case, we calculate the long-time dynamics of the spin current and extract the spin Drude weight for large systems outside the range of ED. We particularly provide strong evidence that the high-temperature Drude weight vanishes at the isotropic point. For the nonintegrable case, we obtain the full relaxation curve of the energy current and determine the heat conductivity as a function of magnetic field, exchange anisotropy, and temperature.