Exact results for nonlinear Drude weights in the spin-1/2 XXZ chain

TL;DR

This paper calculates nonlinear Drude weights in the spin-1/2 XXZ chain, revealing universal divergences linked to nonanalytic finite-size effects, supported by numerical and analytical results.

Contribution

It provides the first comprehensive numerical and analytical analysis of nonlinear Drude weights in the XXZ chain, including divergence behavior and closed-form expressions.

Findings

Divergences in NLDWs occur in all studied orders.

Divergences are due to nonanalytic finite-size corrections.

Analytical formulas agree with numerical results.

Abstract

Nonlinear Drude weight (NLDW) is a new concept which characterizes the nonlinear transport in quantum many-body systems. We investigate these weights for the spin-1/2 XXZ chain in the critical regime. The effects of the Dzyaloshinskii-Moriya interaction and an external magnetic field are also studied. Solving the Bethe equations numerically, we obtain these weights for very large system sizes and identify parameter regimes where the weights diverge in the thermodynamic limit. These divergences appear in all the orders studied in this paper and can be regarded as a universal feature of the NLDWs. We study the origin of these divergences and reveal that they result from $\textit{nonanalytic}$ finite-size corrections to the ground state energy. Furthermore, we compute closed-form expressions for several weights in the thermodynamic limit and find excellent agreement with the numerical results.