Universal broadening of the light cone in low-temperature transport

TL;DR

This paper studies how non-linear effects in low-temperature one-dimensional critical systems modify the traditional light cone picture of energy transport, revealing a universal broadening near the light cone edges.

Contribution

It introduces a non-linear Luttinger liquid framework to describe universal broadening of the light cone in energy transport, extending conformal field theory results.

Findings

Universal broadening of the light cone at finite temperatures.

Explicit universal function describing the smooth peaks.

Agreement with generalized hydrodynamics in integrable models.

Abstract

We consider the low-temperature transport properties of critical one-dimensional systems which can be described, at equilibrium, by a Luttinger liquid. We focus on the prototypical setting where two semi-infinite chains are prepared in two thermal states at small but different temperatures and suddenly joined together. At large distances $x$ and times $t$, conformal field theory characterizes the energy transport in terms of a single light cone spreading at the sound velocity $v$. Energy density and current take different constant values inside the light cone, on its left, and on its right, resulting in a three-step form of the corresponding profiles as a function of $\zeta=x/t$. Here, using a non-linear Luttinger liquid description, we show that for generic observables this picture is spoiled as soon as a non-linearity in the spectrum is present. In correspondence of the transition points $x/t=\pm v$ a novel universal region emerges at infinite times, whose width is proportional to the temperatures on the two sides. In this region, expectation values have a different temperature dependence and show smooth peaks as a function of $\zeta$. We explicitly compute the universal function describing such peaks. In the specific case of interacting integrable models, our predictions are analytically recovered by the generalized hydrodynamic approach.