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The light-cone spreading of entanglement and correlation is a fundamental andubiquitous feature of homogeneous extended quantum systems. Here we point outthat a class of inhomogenous Luttinger liquids (those with a uniform Luttingerparameter $K$) at low energy display the universal phenomenon of curved lightcones: 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 dependentvelocity induced by the inhomogeneity. We confirm our findings with explicitanalytic and numerical calculations both in- and out-of-equilibrium for aTonks-Girardeau gas in a harmonic potential and in lattice systems withartificially tuned hamiltonian density.

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