Fine structure of the nonlinear Drude weights in the spin-1/2 XXZ chain

TL;DR

This paper investigates the nonlinear Drude weights in the critical spin-1/2 XXZ chain, revealing their convergence, divergence, and special anisotropies where they remain finite, using Bethe ansatz and finite-size energy corrections.

Contribution

It provides a detailed analysis of the nonlinear Drude weights' behavior in the XXZ chain, including their divergence patterns and conditions for finiteness at specific anisotropies.

Findings

NLDWs exhibit convergence, power-law, and logarithmic divergence depending on anisotropy.

NLDWs converge for certain response orders and diverge logarithmically for others.

Special anisotropies lead to finite NLDWs at all orders.

Abstract

We study nonlinear Drude weights (NLDWs) for the spin-1/2 XXZ chain in the critical regime at zero temperature. The NLDWs are generalizations of the linear Drude weight. Via the nonlinear extension of the Kohn formula, they can be read off from higher-order finite-size corrections to the ground-state energy in the presence of a $U(1)$ magnetic flux. The analysis of the ground-state energy based on the Bethe ansatz reveals that the NLDWs exhibit convergence, power-law, and logarithmic divergence, depending on the anisotropy parameter $\Delta$. We determine the convergent and power-law divergent regions, which depend on the order of the response $n$. Then, we examine the behavior of the NLDWs at the boundary between the two regions and find that they converge for $n=0, 1, 2$ $({\rm mod}~4)$, while they show logarithmic divergence for $n=3$ $({\rm mod}~4)$. Furthermore, we identify particular anisotropies $\Delta=\cos(\pi r/(r+1))$ ($r=1,2, 3,\ldots$) at which the NLDW at any order $n$ converges to a finite value.