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

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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.

### Most cited references40

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### The Evaluation of the Collision Matrix

(1950)
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### Quantum thermalization through entanglement in an isolated many-body system

,  ,   (2016)
The concept of entropy is fundamental to thermalization, yet appears at odds with basic principles in quantum mechanics. While statistical mechanics relies on the maximization of entropy for a system at thermal equilibrium, an isolated many-body system undergoing Schr\"odinger dynamics has zero entropy because, at any given time, it is described by a single quantum state. The underlying role of quantum mechanics in many-body physics is then seemingly antithetical to the success of statistical mechanics in a large variety of systems. Here we observe experimentally how this conflict is resolved: we perform microscopy on an evolving quantum state, and we see thermalization occur on a local scale, while we measure that the full quantum state remains pure. We directly measure entanglement entropy and observe how it assumes the role of the thermal entropy in thermalization. Although the full state has zero entropy, entanglement creates local entropy that validates the use of statistical physics for local observables. In combination with number-resolved, single-site imaging, we demonstrate how our measurements of a pure quantum state agree with the Eigenstate Thermalization Hypothesis and thermal ensembles in the presence of a near-volume law in the entanglement entropy.
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### Time-dependence of correlation functions following a quantum quench

(2006)
We show that the time-dependence of correlation functions in an extended quantum system in d dimensions, which is prepared in the ground state of some hamiltonian and then evolves without dissipation according to some other hamiltonian, may be extracted using methods of boundary critical phenomena in d+1 dimensions. For d=1 particularly powerful results are available using conformal field theory. These are checked against those available from solvable models. They may be explained in terms of a picture, valid more generally, whereby quasiparticles, entangled over regions of the order of the correlation length in the initial state, then propagate classically through the system.
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### Author and article information

###### Journal
2017-05-01
1705.00679