Multipartite Entanglement Measures and Quantum Criticality from Matrix and Tensor Product States

Abstract

We compute the multipartite entanglement measures such as the global entanglement of various one- and two-dimensional quantum systems to probe the quantum criticality based on the matrix and tensor product states (MPSs/TPSs). We use infinite time-evolving block decimation (iTEBD) method to find the ground states numerically in the form of MPSs/TPSs, and then evaluate their entanglement measures by the method of tensor renormalization group (TRG). We find these entanglement measures can characterize the quantum phase transitions by their derivative discontinuity right at the critical points in all models considered here. We also comment on the scaling behaviors of the entanglement measures by the ideas of quantum state renormalization group transformations.

22 pages, 11 figures

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• Universal short-time quantum critical dynamics in imaginary time
• Topological Order and Degenerate Singular Value Spectrum in Two-Dimensional Dimerized Quantum Heisenberg Model
• Geometric entanglement of critical XXZ and Ising chains and Affleck-Ludwig boundary entropies
• Geometric entanglement and quantum phase transitions in two-dimensional quantum lattice models
• Strong Coupling Expansion of the Entanglement Entropy of Yang-Mills Gauge Theories
• Quantum phase transition in the $Z_3$ Kitaev-Potts model
• Geometric entanglement from matrix product state representations
• Scaling of the Formation Probabilities and Universal Boundary Entropies in the Quantum XY Spin Chain
• Quantum phase transitions in spin-1 compass chains
• Single-ion anisotropy effects on the critical behaviors of quantum entanglement and correlation in the spin-1 Heisenberg chain
• Multicritical behavior of the fidelity susceptibility for the 2D quantum transverse-field $XY$ model
• Tensor-network approach to compute genuine multisite entanglement in infinite quantum spin chains
• Numerical studies of entanglement properties in one- and two-dimensional quantum Ising and XXZ models
• Maximal Overlap with a Fully Separable State and Translational Invariance in Multipartite Entangled States
• Overlap with the Separable State and Phase Transition in the Dicke Model: Zero and Finite Temperature
• Measuring multipartite quantum correlations by thermodynamic work extraction
• Efficient optimization and conceptual barriers in variational finite Projected Entangled-Pair States
• Geometric Entanglement in Valance-Bond-Solid state
• Entanglement Entropy and Quantum Phase Transition in the $O(N)$ $\sigma$-model