Universal broadening of the light cone in low-temperature transport

Bruno Bertini, Lorenzo Piroli, Pasquale Calabrese

Published 2017-09-28Version 1

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 predicts universal profiles of the energy density and current: a single light cone emerges, resulting in a three-step form of the profiles, with sharp transitions at the edges. Here we provide a generalization to arbitrary observables, which is obtainable by taking into account the generic nonlinearity of the spectrum. Using a universal nonlinear Luttinger liquid description, we show that generic observables still display a three-step form, but smooth peaks emerge at the edges of the light cone. These are described by a universal function of $\zeta=x/t$ which we compute explicitly. In the case of interacting integrable models, we show that our predictions agree with the results of the generalized hydrodynamic approach.