# Bounding entanglement spreading after a local quench

## TL;DR

This paper derives bounds on how quickly entanglement spreads in many-body quantum systems after a local quench, showing it is limited by an effective light cone independent of subsystem size.

## Contribution

It introduces volume-independent Lieb-Robinson-like bounds for entanglement growth after local quenches in lattice spin systems.

## Key findings

- Entanglement growth is exponentially bounded in time and distance.
- Entanglement propagation obeys an effective light cone regardless of system size.
- Implications for quantum simulation and information propagation are discussed.

## Abstract

We consider the variation of von Neumann entropy of subsystem reduced states of general many- body lattice spin systems due to local quantum quenches. We obtain Lieb-Robinson-like bounds that are independent of the subsystem volume. The main assumptions are that the Hamiltonian satisfies a Lieb-Robinson bound and that the volume of spheres on the lattice grows at most exponentially with their radius. More specifically, the bound exponentially increases with time but exponentially decreases with the distance between the subsystem and the region where the quench takes place. The fact that the bound is independent of the subsystem volume leads to stronger constraints (than previously known) on the propagation of information throughout many-body systems. In particular, it shows that bipartite entanglement satisfies an effective "light cone", regardless of system size. Further implications to t density-matrix renormalization-group simulations of quantum spin chains and limitations to the propagation of information are discussed.