Entanglement links and the quasiparticle picture

TL;DR

This paper extends the quasi-particle picture of entanglement spreading to initial states with long-range correlations using a link representation, enabling predictions of entanglement dynamics in more complex quantum states.

Contribution

It introduces a novel link representation of entanglement that generalizes the quasi-particle picture to long-range correlated initial states.

Findings

The link representation obeys a wave equation, enabling analytical predictions.

Numerical checks confirm the model's accuracy for free fermionic chains.

The approach broadens understanding of entanglement dynamics beyond short-range correlations.

Abstract

The time evolution of a quantum state with short-range correlations after a quench to a one-dimensional critical Hamiltonian can be understood using the quasi-particle picture, which states that local entanglement spreads as if it was carried by quasi-particles which separate at a fixed speed. We extend the quasi-particle picture using the recently introduced link representation of entanglement, allowing us to apply it to initial states presenting long-range correlations. The entanglement links are current correlators, and therefore follow a wave equation on the appropriate configurational space which allows us to predict the time evolution of the entanglement entropies. Our results are checked numerically for free fermionic chains with different initial entanglement patterns.