Continuum limit, Galilean invariance, and solitons in the quantum equivalent of the noisy Burgers equation

TL;DR

This paper derives a continuum limit of a non-Hermitian spin chain related to the noisy Burgers equation, demonstrating Galilean invariance and discovering soliton excitations with specific dispersion properties.

Contribution

It provides a rigorous continuum limit of a non-Hermitian spin chain within the noisy Burgers universality class, explicitly realizing Galilean invariance and identifying soliton solutions.

Findings

Continuum limit of the non-Hermitian spin-1/2 chain obtained.

Galilean invariance explicitly realized in the operator algebra.

Identification of nonlinear soliton excitations with specific dispersion relation.

Abstract

A continuum limit of the non-Hermitian spin-1/2 chain, conjectured recently to belong to the universality class of the noisy Burgers or, equivalently, Kardar-Parisi-Zhang equation, is obtained and analyzed. The Galilean invariance of the Burgers equation is explicitly realized in the operator algebra. In the quasi-classical limit we find nonlinear soliton excitations exhibiting the $\omega\propto k^z$ dispersion relation with dynamical exponent $z=3/2$.