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

## TL;DR

This paper demonstrates that inhomogeneous Luttinger liquids with constant Luttinger parameter exhibit curved light cones due to spatially varying velocities, confirmed through analytic and numerical methods in different systems.

## Contribution

It reveals the universal emergence of curved light cones in a specific class of inhomogeneous Luttinger liquids, linking geometry with quantum dynamics.

## Key findings

- Inhomogeneous Luttinger liquids show curved light cones.
- Analytic and numerical results confirm geodesic propagation.
- Applicable to Tonks-Girardeau gases and lattice systems.

## 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.