Entanglement transition in a cluster spin chain coupled with free spins

TL;DR

This paper explores how entanglement in a spin ladder system transitions between different phases depending on coupling strength, revealing a shift from topological states to mixed states as interactions intensify.

Contribution

It introduces a model of a spin ladder with combined automaton dynamics and identifies entanglement phase transitions driven by coupling variations.

Findings

Weak coupling maintains topological cluster states

Strong coupling results in random, mixed states

Entanglement phases depend on interaction strength

Abstract

We investigate the entanglement of a ladder of spins formed by two sublattices, a ''cluster'' chain and the ''environment'', consisting of independent spins, both coupled by an exchange interaction and evolving under a unitary discrete time dynamics. The automaton is defined by the composition of the two body spin swap gate (between sublattices) and the three body cluster interaction. We observe that, depending on the set of coupling constants, the cluster subsystem evolves towards states corresponding to different entanglement phases. In the weak coupling regime the subsystem remains near the topological cluster state. Increasing the coupling strength leads to random states which transform from almost pure to fully mixed, according to the effective number of the environment active degrees of freedom.