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Persistent Multipartite Entanglement in a Quantum Spin System

Jiang Zhou, Hong Mei Guo

Published Jan 1, 2013• 0 citations
Publisher

Abstract

We find the very eigenspaces where multipartite entanglement is more persistent than the bipartite entanglement and can even evolve into a specific constant in a model many-spin systems decohered by a thermal bath.
DOI
10.1364/cleo_qels.2013.jth2a.82

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The time evolution of genuine multipartite entanglement is numerically studied in a model many-spin system decohered by a structured spin bath. It is found that multipartite entanglement can be more persistent than the bipartite entanglement and can even evolve into a specific constant under certain conditions. Besides, multipartite entanglement sudden death and sudden birth are observed. It is shown that the randomness of the coupling strength and connectivity between the spins in the environment will suppress these birth and death phenomena. Furthermore, the initial state of the central system plays a significant role in determining multipartite entanglement dynamics.
We derive the entangled thermal mixed states by using the formalism of phase states for a finite-dimensional algebra of a multi-qubit system in contact with an independent thermal environment of absolute temperature [Formula: see text]. Thermal entangled states describing the multi-qubit system in equilibrium with the thermal bath are a special kind of mixed states that exhibit genuine multipartite correlation. We define the unitary phase operators for a multipartite system of non-interacting qubits. Entangled density matrices are derived for qubits interacting via an Hermitian Hamiltonian of Heisenberg type [Formula: see text]. By assuming that the noisy interaction of the entangled qubit ensemble with the bath is governed by a local Hamiltonian [Formula: see text], we show that the entangled phase states can be decohered. When the multi-qubits entangled system reaches the equilibrium with the thermal bath, the decohered mixed states are identified with entangled thermal states. The thermal mixed states for bipartite and multipartite systems are explicitly expressed and their bipartite entanglement properties are investigated.
Abstract Multipartite entanglement (ME) in the XY spin-1/2 chain is investigated by using negativity as a quantitative measure. The results show that ME persists over longer distances than bipartite entanglement, with its range and strength dependent on the anisotropy parameter γ, external magnetic field h, and the size of spin blocks. Notably, ME could serve as a sensitive probe for quantum phase transitions, due to the divergent behavior in its first derivative at the critical point h = 1. In essence, ME may primarily derive from collective effects rather than pairwise spin-spin entanglement, particularly in disjoint spin configurations. At finite temperatures and γ= 1, the thermal suppression of ME follows a hierarchical pattern, and such suppression is further modulated by ℎ and the specific block geometries. This behavior challenges the conventional conjecture of a simplistic monotonic decay.