Abstract
We devise a method based on the tensor-network formalism to calculate genuine multisite entanglement in ground states of infinite spin chains containing spin-1/2 or spin-1 quantum particles. The ground state is obtained by employing an infinite time-evolving block decimation method acting upon an initial matrix product state for the infinite spin system. We explicitly show how such infinite matrix product states with translational invariance provide a natural framework to derive the generalized geometric measure, a computable measure of genuine multisite entanglement, in the thermodynamic limit of quantum many-body systems with both spin-1/2 and higher-spin particles.
Highlights
In recent years, entanglement [1] has turned out to be an important characteristic in the study of lowdimensional strongly-correlated quantum systems, especially from the perspective of critical phenomena in the low-temperature regime of many quantum many-body systems [2,3,4,5] and implementation of quantum information protocols using solid-state, cold gas, and other physical substrates [6,7,8,9,10]
We show that matrix product states for infinite one-dimensional quantum spin systems, provide a natural framework to estimate the generalized geometric measure (GGM) [19], which is a computable measure of genuine multipartite entanglement, defined by using the geometry of the space of multiparty states
We have shown how the tensor-network approach provides a natural structure to study genuine multiparty entanglement, quantified by generalized geometric measure, in many-body quantum systems
Summary
Entanglement [1] has turned out to be an important characteristic in the study of lowdimensional strongly-correlated quantum systems, especially from the perspective of critical phenomena in the low-temperature regime of many quantum many-body systems [2,3,4,5] and implementation of quantum information protocols using solid-state, cold gas, and other physical substrates [6,7,8,9,10]. We employ a tensor-network based approach to estimate the genuine multipartite entanglement, which for pure quantum states characterizes the situation where the many-body system cannot be formed by states that are product across some bipartition(s) of the multiparty system. We investigate this behavior in the thermodynamic limit of infinite chains of both spin1/2 as well as spin-1 quantum systems.
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