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

2017/05/31 by Jérôme Dubail, Jean-Marie Stéphan, Pasquale Calabrese · 2 citations
Physics and Astronomy · #cond-mat.str-el #cond-mat.quant-gas #quant-ph

paper · pdf · doi:10.21468/scipostphys.3.3.019

published as SciPost Phys. 3, 019 (2017) · v1: 20 pages + refs, 7 figures. v2: references added. v3: minor changes

arxiv created 2017/07/12 · arxiv updated 2017/09/07

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 ds²=dx²+v(x)² dτ², 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.

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