Hydrodynamic nonlinear response of interacting integrable systems

We develop a formalism for computing the nonlinear 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.

Automated summary

The study establishes a formalism for computing the nonlinear response of interacting integrable systems, showing results that are asymptotically exact in the hydrodynamic limit. Spatially resolved nonlinear responses can distinguish interacting integrable systems from noninteracting ones, with a method for computing finite-temperature Drude weights and identifying nonperturbative regimes of the nonlinear response.