Kardar-Parisi-Zhang universality from soft gauge modes

TL;DR

This paper demonstrates that soft gauge modes in isotropic integrable magnets exhibit Kardar-Parisi-Zhang universality, explaining superdiffusive spin dynamics through a novel hydrodynamic framework.

Contribution

It introduces soft gauge degrees of freedom into hydrodynamic descriptions of integrable magnets, linking them to KPZ universality class.

Findings

Soft gauge modes arise from spontaneous symmetry breaking.

These modes follow KPZ universality class dynamics.

Hydrodynamics of integrable magnets includes previously overlooked gauge degrees of freedom.

Abstract

The emergence of superdiffusive spin dynamics in integrable classical and quantum magnets is well established by now, but there is no generally valid theoretical explanation for this phenomenon. A fundamental difficulty is that the hydrodynamic fluctuations of conserved quasiparticle modes are purely diffusive. We argue that in isotropic integrable magnets, a complete hydrodynamic description must include soft "gauge" degrees of freedom, that arise from spontaneous breaking of the Bethe pseudovacuum symmetry. We show that the coarse-grained time evolution of these modes lies in the Kardar-Parisi-Zhang universality class of dynamics.