Nonlinear entanglement growth in inhomogeneous spacetimes

TL;DR

This paper investigates how inhomogeneous spacetimes, like those near black holes, cause entanglement growth in quantum systems to become sublinear and alter relaxation dynamics, revealing new universal behaviors.

Contribution

It demonstrates that inhomogeneous spacetimes lead to sublinear entanglement growth and exponential relaxation, extending understanding beyond planar geometries.

Findings

Entanglement growth is sublinear in inhomogeneous spacetimes.

Relaxation becomes exponential near black holes.

Large subsystems relax independently of size.

Abstract

Entanglement has become central for the characterization of quantum matter both in and out of equilibrium. In a dynamical context entanglement exhibits universal linear temporal growth in generic systems, which stems from the underlying linear light cones as they occur in planar geometries. Inhomogeneous spacetimes can lead, however, to strongly bent trajectories. While such bent trajectories crucially impact correlation spreading and therefore the light-cone structure, it has remained elusive how this influences the entanglement dynamics. In this work we investigate the real-time evolution of the entanglement entropy in one-dimensional quantum systems after quenches which change the underlying spacetime background of the Hamiltonian. Concretely, we focus on the Rindler space describing the spacetime in close vicinity to a black hole. As a main result we find that entanglement grows sublinearly in a generic fashion both for interacting and noninteracting quantum matter. We further observe that the asymptotic relaxation becomes exponential, as opposed to algebraic for planar Minkowski spacetimes, and that in the vicinity of the black hole the relaxation time for large subsystems becomes independent of the subsystem size. We study entanglement dynamics both for the case of noninteracting fermions, allowing for exact numerical solutions, and for random unitary circuits representing a paradigmatic class of ergodic systems.