Genuine tripartite entanglement as a probe of quantum phase transitions in a spin-1 Heisenberg chain with single-ion anisotropy

Abstract

We study the quantum phase transitions of spin-1 Heisenberg chains with an easy-axis anisotropy $\Delta$ and a uniaxial single-ion anisotropy $D$ 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 $\Delta -D$ plane with $\Delta >0$. 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 justifies the usage of genuine multipartite entanglement as a probe of topological phases in spin systems.

References in corpus (42)

• Quantum entanglement
• Entanglement of Formation of an Arbitrary State of Two Qubits
• Three qubits can be entangled in two inequivalent ways
• Entanglement of a Pair of Quantum Bits
• Distributed Entanglement
• Topological entanglement entropy
• Detecting topological order in a ground state wave function
• Entanglement spectrum of a topological phase in one dimension
• Zoo of quantum-topological phases of matter
• Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order
• Fidelity approach to quantum phase transitions
• Classical Correlation and Quantum Discord in Critical Systems
• Quantum critical scaling of the geometric tensors
• Quantum enhanced measurements without entanglement
• Quantum discord and quantum phase transition in spin chains
• Classification of multipartite entangled states by multidimensional determinants
• Ground State Phase Diagram of S=1 XXZ Chains with Uniaxial Single-Ion-Type Anisotropy
• Multipartite entanglement in spin chains
• Quantum and classical thermal correlations in the XY spin-1/2 chain
• Dzyaloshinskii-Moriya Interaction and Anisotropy effects on the Entanglement of Heisenberg Model
• Coherent electrical control of a single high-spin nucleus in silicon
• The renormalization of entanglement in the anisotropic Heisenberg (XXZ) model
• Scaling Properties of Fidelity in Spin-one Anisotropic Model
• Renormalization of concurrence: the application of quantum renormalization group to the quantum information systems
• Phase Diagram of $S=1$ Bond-Alternating XXZ chains
• Multipartite entanglement in quantum spin chains
• Analytic Formulations of the Density Matrix Renormalization Group
• Accurate determination of the Gaussian transition in spin-1 chains with single-ion anisotropy
• The moduli space of three qutrit states
• Fidelity approach to Gaussian transitions
• Quasiperiodic dynamical quantum phase transitions in multiband topological insulators and connections with entanglement entropy and fidelity susceptibility
• Topological transitions from multipartite entanglement with tensor networks: a procedure for sharper and faster characterization
• Ground-state fidelity at first-order quantum transitions
• Ground-state fidelity of the spin-1 Heisenberg chain with single ion anisotropy: quantum renormalization group and exact diagonalization approaches
• Geometric Entanglement in Topologically Ordered States
• Quantum Phase Transition and Entanglement in Topological Quantum Wires
• Quantum phase transitions in a spin-1 antiferromagnetic chain with long-range interactions and modulated single-ion anisotropy
• Classification scheme of pure multipartite states based on topological phases
• Three-Tangle of a General Three-Qubit State in the Representation of Majorana Stars
• The 3 x 3 x 3 hyperdeterminant as a polynomial in the fundamental invariants for SL(3,C) x SL(3,C) x SL(3,C)
• Single-ion anisotropy effects on the critical behaviors of quantum entanglement and correlation in the spin-1 Heisenberg chain
• Bell-type correlation at quantum phase transitions in spin-1 chain