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 KK) at low energy display the universal phenomenon of curved light cones: gapless excitations propagate along the null geodesics of the metric ds^2 = dx^2 - v(x)^2 dt^2ds2=dx2−v(x)2dt2, with v(x)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.
Highlights
Light-cone propagation of signals in condensed matter and cold atom physics has attracted a lot of attention in the past decade
Apart from the Lieb-Robinson rigorous mathematical bound, condensed matter systems sometimes display the same behavior as relativistic models of high-energy physics: this happens at quantum critical points with dynamic exponent z = 1, where emergent massless quasiparticles propagate at a critical velocity v which plays the same role as the speed of light in high-energy physics
Assumptions in this paper: 1. the parameter K is uniform, i.e. it does not depend on position (x, τ) in spacetime; large-scale correlations can be obtained from the action (7); 2. we consider small perturbations around the ground state of H; the entries of the metric tensor g do not depend on time τ; 3. the system is time-reversal invariant; the component gxτ of the metric tensor is zero
Summary
Light-cone propagation of signals in condensed matter and cold atom physics has attracted a lot of attention in the past decade. Apart from the Lieb-Robinson rigorous mathematical bound, condensed matter systems sometimes display the same behavior as relativistic models of high-energy physics: this happens at quantum critical points with dynamic exponent z = 1, where emergent massless quasiparticles propagate at a critical (sound) velocity v which plays the same role as the speed of light in high-energy physics This relativistic behavior emerges only when probing the lowenergy (large distance) universal features of these systems. We focus on two particular microscopic realizations of an inhomogeneous Luttinger liquid: impenetrable bosons in a non-uniform trap potential, and spin chains with position-dependent couplings between neighboring spins These two systems share a crucial property, on which our entire analysis is relying: the Luttinger parameter K is constant in those systems.
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