Entanglement Propagation in Integrable Heisenberg Chains from a New Lens

TL;DR

This paper introduces a novel analytical approach using the Quantum Correlation Transfer Function to study entanglement dynamics in Heisenberg chains, revealing early quasi-particle contributions and extending to multi-magnon regimes.

Contribution

It presents a new frequency and time-domain analysis method for entanglement evolution in Heisenberg chains, bypassing full state evaluation and revealing faster-than-expected quasi-particle effects.

Findings

Transient entanglement dynamics described by Bessel functions.

Early quasi-particles travel faster than the maximum group velocity.

Method can be extended to multi-magnon regimes.

Abstract

The exact single-magnon entanglement evolution in Heisenberg chains is obtained using the Quantum Correlation Transfer Function (QCTF) formulation. A dual, i.e., frequency and time-domain, analysis shows that the transient dynamics of individual spins' entanglement is described via a Bessel function of the first kind. Through QCTF, we bypass the evaluation of the full system's state for the purpose of obtaining entanglement. Although it is known that the observable entanglement edge is formed by the arrival of a stream of quasi-particles that travel with the maximum group velocity, we show how the early quasi-particles travel faster than the maximum group velocity of the chain and contribute to entanglement production. Our results can be extended to the multi-magnon regime, therefore opening up the means to better interpret equilibration dynamics and thermodynamics in Heisenberg chains.