Hydrodynamic non-linear response of interacting integrable systems

TL;DR

This paper develops a formalism to compute the non-linear hydrodynamic response of interacting integrable systems, revealing unique spatially resolved nonlinear behaviors and providing methods to calculate higher-order transport coefficients.

Contribution

It introduces a novel formalism for asymptotically exact non-linear response calculations in integrable systems, including a prescription for finite-temperature Drude weights and identification of nonperturbative regimes.

Findings

Spatially resolved nonlinear response distinguishes integrable from noninteracting systems.

The formalism accurately predicts third-order response in the XXZ spin chain.

The approach provides a way to compute higher-order Drude weights at finite temperature.

Abstract

We develop a formalism for computing the non-linear response of interacting integrable systems. Our results are asymptotically exact in the hydrodynamic limit where perturbing fields vary sufficiently slowly in space and time. We show that spatially resolved nonlinear response distinguishes interacting integrable systems from noninteracting ones, exemplifying this for the Lieb-Liniger gas. We give a prescription for computing finite-temperature Drude weights of arbitrary order, which is in excellent agreement with numerical evaluation of the third-order response of the XXZ spin chain. We identify intrinsically nonperturbative regimes of the nonlinear response of integrable systems.