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arXiv · 1705.00679

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

Jérôme Dubail·Jean-Marie Stéphan·Pasquale Calabrese
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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.

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Jérôme Dubail, Jean-Marie Stéphan, Pasquale Calabrese. 2017-05-01. Emergence of curved light-cones in a class of inhomogeneous Luttinger liquids. https://doi.org/10.21468/scipostphys.3.3.019

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