A genuine tripartite entanglement monotone is presented for $(2\ensuremath{\bigotimes}2\ensuremath{\bigotimes}n)$-dimensional tripartite pure states, obtained by introducing an entanglement measure for bipartite pure states. As an application, we consider the genuine tripartite entanglement of the ground state of the exactly solvable isotropic spin- $1/2$ chain with three-spin interaction. It is shown that the singular behavior of the genuine tripartite entanglement exactly signals a quantum phase transition.A genuine tripartite entanglement monotone is presented for $(2\ensuremath{\bigotimes}2\ensuremath{\bigotimes}n)$-dimensional tripartite pure states, obtained by introducing an entanglement measure for bipartite pure states. As an application, we consider the genuine tripartite entanglement of the ground state of the exactly solvable isotropic spin-$1/2$ chain with three-spin interaction. It is shown that the singular behavior of the genuine tripartite entanglement exactly signals a quantum phase transition.

arXiv:0802.1975Physical Review AFeb 13, 200812 citations

Genuine Tripartite Entanglement as a Probe of Quantum Phase Transitions in a Spin‐1 Heisenberg Chain with Single‐Ion Anisotropy

Chon‐Fai Kam, Yang Chen

Abstract The quantum phase transitions of spin‐1 Heisenberg chains with an easy‐axis anisotropy Δ and a uniaxial single‐ion anisotropy D are studied using a multipartite entanglement approach. The genuine tripartite entanglement between the spin blocks, measured by the tripartite qutrit hyperdeterminant, is calculated within the quantum renormalization group method. Using this approach, the phase boundaries between the topological Haldane, large‐D, and anti‐ferromagnetic Néel phases are determined in the half plane with . When the size of the spin blocks increases, the genuine tripartite entanglement between the blocks exhibits a nonzero plateau in the topological Haldane phase, and experiences abrupt drops at both the phase boundaries between the Haldane–large‐D and Haldane–Néel phases, which suggests the usage of genuine multipartite entanglement as a probe of topological phases in spin systems.Abstract The quantum phase transitions of spin‐1 Heisenberg chains with an easy‐axis anisotropy Δ and a uniaxial single‐ion anisotropy D are studied using a multipartite entanglement approach. The genuine tripartite entanglement between the spin blocks, measured by the tripartite qutrit hyperdeterminant, is calculated within the quantum renormalization group method. Using this approach, the phase boundaries between the topological Haldane, large‐D, and anti‐ferromagnetic Néel phases are determined in the half plane with . When the size of the spin blocks increases, the genuine tripartite entanglement between the blocks exhibits a nonzero plateau in the topological Haldane phase, and experiences abrupt drops at both the phase boundaries between the Haldane–large‐D and Haldane–Néel phases, which suggests the usage of genuine multipartite entanglement as a probe of topological phases in spin systems.

arXiv:2106.10690Annalen der PhysikFeb 24, 20224 citations

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chain with three-spin interaction. It is shown that the singular behavior of the genuine tripartite entanglement exactly signals a quantum phase transition.