Numerical studies of entanglement properties in one- and two-dimensional quantum Ising and XXZ models

Abstract

We investigate entanglement properties of infinite 1D and 2D spin-1/2 quantum Ising and XXZ models. Tensor network methods (MPS in 1D and TERG and CTMRG in 2D) are used to model the ground state of the studied models. Different entanglement measures, such as one-site entanglement entropy, one-tangle, concurrence of formation and assistance, negativity and entanglement per bond are calculated and their `characterizing power' to determine quantum phase transitions is compared. A special emphasis is made on the study of entanglement monogamy properties.

19 pages, 24 figures

References in corpus (23)

• The density-matrix renormalization group in the age of matrix product states
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• "Deconfined" quantum critical points
• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
• Tensor renormalization group approach to 2D classical lattice models
• Quantum Phase Transitions and Bipartite Entanglement
• Accurate determination of tensor network state of quantum lattice models in two dimensions
• Entanglement versus Correlations in Spin Systems
• Tensor-entanglement renormalization group approach to 2D quantum systems
• Entanglement of assistance and multipartite state distillation
• Entanglement monogamy relations of qubit systems
• Quantum Monte Carlo simulations of fidelity at magnetic quantum phase transitions
• Duality for monogamy of entanglement
• Entanglement and factorized ground states in two-dimensional quantum antiferromagnets
• Divergence of the entanglement range in low dimensional quantum systems
• Strong monogamy conjecture for multiqubit entanglement: The four-qubit case
• Efficient simulation of infinite tree tensor network states on the Bethe lattice
• Two-spin entanglement distribution near factorized states
• Enhancement of pairwise entanglement from $\mathbbm{Z}_2$ symmetry breaking
• Quantum phase transitions in a two-dimensional quantum XYX model: Ground-state fidelity and entanglement

Cited by in corpus (5)

• Two-dimensional quantum-spin-1/2 XXZ magnet in zero magnetic field: global thermodynamics from renormalization group theory
• Entanglement Microscopy: Tomography and Entanglement Measures via Quantum Monte Carlo
• Study of Staggered Magnetization in the Spin-$S$ Square-Lattice Heisenberg Model Using Spiral Boundary Conditions
• Comparing quantum fluctuations in the spin-$\frac{1}{2}$ and spin-$1$ XXZ Heisenberg models on square and honeycomb lattices
• Multiparty Entanglement Microscopy of Quantum Ising models in 1d, 2d and 3d