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Physics Letters A

Effects of three-body interactions on the dynamics of entanglement in spin chains

Cui-Hua Shi, Yin‐Zhong Wu, Zhenya Li

Published Jun 9, 2009• 6 citations
Publisher
DOI
10.1016/j.physleta.2009.06.012

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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.
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.
In this paper, we diagonalize the Hamiltonian of the one-dimensional spin chain system with three-body interaction. Then we solve geometric phase of ground state in the system through a rotating operation. By the numerical calculation of the geometric phase and its derivative, we consider the three-body interaction effects on the geometric phase and quantum phase transition, the results show that the geometric phase can be well used to characterize quantum phase transition in this system, and find that three-body interaction not only can move the criticality region, but also can generate a new critical point.