Universal Broadening of the Light Cone in Low-Temperature Transport

Physical Review Letters
Bruno BertiniPasquale Calabrese

Abstract

We consider the low-temperature transport properties of critical one-dimensional systems that 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 ζ=x/t. Here, using a nonlinear Luttinger liquid description, we show that for generic observables this picture is spoiled as soon as a nonlinearity in the spectrum is present. In correspondence of the transition points x/t=±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 ζ. We explicitly compute the universal function describing such peaks. In the specific case of interacting integrable m...Continue Reading

References

May 23, 2006·Physical Review Letters·Pasquale Calabrese, John Cardy
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Jul 13, 2017·Proceedings of the National Academy of Sciences of the United States of America·Vincenzo Alba, Pasquale Calabrese
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Feb 14, 2018·Physical Review Letters·Benjamin DoyonJean-Sébastien Caux
Feb 27, 2018·Physical Review Letters·Alvise Bastianello, Andrea De Luca

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Citations

Nov 6, 2018·Physical Review Letters·Jacopo De NardisBenjamin Doyon
Apr 28, 2020·Physical Review Letters·Paola RuggieroJérôme Dubail
Jun 9, 2018·Physical Review Letters·Jacopo De Nardis, Miłosz Panfil
Nov 8, 2019·Physical Review Letters·Alvise BastianelloJean-Sébastien Caux
Jul 20, 2019·Physical Review Letters·Alvise Bastianello, Andrea De Luca

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