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Entanglement transition in a cluster spin chain coupled with free spins

Kevissen Sellapillay*

Laurent Raymond† and Alberto D. Verga‡

  • *Contact author: k.sellapillay@fz-juelich.de
  • †Contact author: laurent.raymond@univ-amu.fr
  • ‡Contact author: alberto.verga@univ-amu.fr
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Phys. Rev. B 112, 104302 – Published 2 September, 2025

DOI: https://doi.org/10.1103/cw4n-b8xc

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 that transform from almost pure to fully mixed, according to the effective number of the environment's active degrees of freedom.

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Phys. Rev. B 112, 104302– Published 2 September, 2025
  • Received 31 January 2025
  • Revised 10 June 2025
  • Accepted 13 August 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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