标题： 簇自旋链与自由自旋的纠缠相变 显示英文标题

标题： Entanglement transition in a cluster spin chain coupled with free spins

摘要： 我们研究由两个亚格子形成的自旋梯子的纠缠，一个“簇”链和一个“环境”，由独立自旋组成，两者通过交换相互作用耦合，并在单位离散时间动力学下演化。 该自动机由两个体自旋交换门（在亚格子之间）和三个体簇相互作用组成。 我们观察到，根据耦合常数的集合，簇子系统会演化为对应不同纠缠相的状态。 在弱耦合区域，子系统保持在拓扑簇态附近。 增加耦合强度会导致从几乎纯态到完全混合态的随机态，这取决于环境活跃自由度的有效数量。 显示英文摘要

摘要： 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.