Emergence of curved light-cones in a class of inhomogeneous Luttinger liquids

Dubail, Jerome; Stéphan, Jean-Marie; Calabrese, Pasquale

doi:10.21468/SciPostPhys.3.3.019

SciPost Physics

Emergence of curved light-cones in a class of inhomogeneous Luttinger liquids

Jérôme Dubail, Jean-Marie Stéphan, Pasquale Calabrese

SciPost Phys. 3, 019 (2017) · published 6 September 2017

doi: 10.21468/SciPostPhys.3.3.019
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Abstract

The light-cone spreading of entanglement and correlation is a fundamental and ubiquitous feature of homogeneous extended quantum systems. Here we point out that a class of inhomogenous Luttinger liquids (those with a uniform Luttinger parameter $K$) at low energy display the universal phenomenon of curved light cones: gapless excitations propagate along the geodesics of the metric $ds^2=dx^2+v(x)^2 d\tau^2$, with $v(x)$ being the calculable spatial dependent velocity induced by the inhomogeneity. We confirm our findings with explicit analytic and numerical calculations both in- and out-of-equilibrium for a Tonks-Girardeau gas in a harmonic potential and in lattice systems with artificially tuned hamiltonian density.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.3.3.019
TI  - Emergence of curved light-cones in a class of inhomogeneous Luttinger liquids
PY  - 2017/09/06
UR  - https://scipost.org/SciPostPhys.3.3.019
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 3
IS  - 3
SP  - 019
A1  - Dubail, Jerome
AU  - Stéphan, Jean-Marie
AU  - Calabrese, Pasquale
AB  - The light-cone spreading of entanglement and correlation is a fundamental and ubiquitous feature of homogeneous extended quantum systems. Here we point out that a class of inhomogenous Luttinger liquids (those with a uniform Luttinger parameter $K$) at low energy display the universal phenomenon of curved light cones: gapless excitations propagate along the geodesics of the metric $ds^2=dx^2+v(x)^2 d\tau^2$, with $v(x)$ being the calculable spatial dependent velocity induced by the inhomogeneity. We confirm our findings with explicit analytic and numerical calculations both in- and out-of-equilibrium for a Tonks-Girardeau gas in a harmonic potential and in lattice systems with artificially tuned hamiltonian density.
ER  -

@Article{10.21468/SciPostPhys.3.3.019,
	title={{Emergence of curved light-cones in a class of inhomogeneous Luttinger liquids}},
	author={Jérôme Dubail and Jean-Marie Stéphan and Pasquale Calabrese},
	journal={SciPost Phys.},
	volume={3},
	pages={019},
	year={2017},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.3.3.019},
	url={https://scipost.org/10.21468/SciPostPhys.3.3.019},
}

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Ontology / Topics

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Entanglement Spatially inhomogeneous systems Tomonaga-Luttinger liquids Tonks-Girardeau gas

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Funders for the research work leading to this publication