Continuum Limit, Galilean Invariance, and Solitons in the Quantum Equivalent of the Noisy Burgers Equation

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 quasiclassical limit we find nonlinear soliton excitations exhibiting the $\omega \propto k^z$ dispersion relation with dynamical exponent $z=3\mathrm{}/2$.