Zero-frequency transport properties of one dimensional spin-1/2 systems

TL;DR

This paper investigates the zero-frequency transport properties, specifically Drude weights, in one-dimensional spin-1/2 systems, revealing finite spin Drude weight in integrable models and vanishing in non-integrable ones, through analytical and numerical methods.

Contribution

It provides a comprehensive analysis of transport in both integrable and non-integrable 1D spin-1/2 systems using multiple theoretical and numerical approaches.

Findings

Finite spin Drude weight in the isotropic integrable chain.

Drude weights vanish in the thermodynamic limit for non-integrable models.

Comparison of numerical results with Bethe ansatz and bosonization methods.

Abstract

We report a detailed analysis of the Drude weights for both thermal and spin transport in one dimensional spin-1/2 systems by means of exact diagonalization and analytic approaches at finite temperatures. Transport properties are studied first for the integrable XXZ model and second for various non-integrable systems such as the dimerized chain, the frustrated chain, and the spin ladder. We compare our results obtained by exact diagonalization and mean-field theory with the Bethe ansatz, bosonization and other numerical studies in the case of the anisotropic Heisenberg model both in the gapless and gapped regime. In particular, we find indications that the Drude weight for spin transport is finite in the thermodynamic limit for the isotropic chain. For the non-integrable models, a finite-size analysis of the numerical data for the Drude weights is presented covering the entire parameter space of the dimerized and frustrated chain. We also discuss which conclusions can be drawn from bosonization regarding the question whether the Drude weights are finite or not. One of our main results is that the Drude weights vanish in the thermodynamic limit for non-integrable models.