Geometric entanglement and quantum phase transitions in two-dimensional quantum lattice models

Abstract

Geometric entanglement(GE), as a measure of multipartite entanglement, has been investigated as a universal tool to detect phase transitions in quantum many-body lattice models. We outline a systematic method to compute GE for two-dimensional (2D) quantum many-body lattice models based on the translational invariant structure of infinite projected entangled pair state (iPEPS) representations. By employing this method, the $q$-state quantum Potts model on the square lattice with $q\in \{2,3,4,5\}$ is investigated as a prototypical example. Further, we have explored three 2D Heisenberg models, such as the spin-$\frac{1}{2}$ XXX and antiferromagnetic anisotropic XYX models in an external magnetic field, and the spin-1 antiferromagnetic XXZ model. We find that continuous GE does not guarantee a continuous phase transition across a phase transition point. We observe and thus classify three different types of continuous GE across a phase transition point: (i) GE is continuous with maximum value at the transition point and the phase transition is continuous, (ii) GE is continuous with maximum value at the transition point but the phase transition is discontinuous, and (iii) GE is continuous with non-maximum value at the transition point and the phase transition is continuous. For the models under consideration we find that the second and the third types are related to a point of dual symmetry and a fully polarized phase, respectively.

arXiv comment11 pages, 9 figures, minor changes, additional figure and references, and clarification of relation to arXiv:1106.2129

References in corpus (39)

• Efficient classical simulation of slightly entangled quantum computations
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Efficient simulation of one-dimensional quantum many-body systems
• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• Time-dependent variational principle for quantum lattices
• Geometric measure of entanglement and applications to bipartite and multipartite quantum states
• Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
• DMRG and periodic boundary conditions: a quantum information perspective
• Computational Studies of Quantum Spin Systems
• Accurate determination of tensor network state of quantum lattice models in two dimensions
• The iTEBD algorithm beyond unitary evolution
• Computing quantum discord is NP-complete
• Variational study of hard-core bosons in a 2-D optical lattice using Projected Entangled Pair States (PEPS)
• Monotones and invariants for multi-particle quantum states
• The iPEPS algorithm, improved: fast full update and gauge fixing
• Equivalence of critical scaling laws for many-body entanglement in the Lipkin-Meshkov-Glick model
• Ground state fidelity from tensor network representations
• Global entanglement and quantum criticality in spin chains
• Advances on Tensor Network Theory: Symmetries, Fermions, Entanglement, and Holography
• Loop updates for variational and projector quantum Monte Carlo simulations in the valence-bond basis
• Entanglement and factorized ground states in two-dimensional quantum antiferromagnets
• How universal is the entanglement spectrum?
• Universal geometric entanglement close to quantum phase transitions
• Efficient Matrix Product State Method for periodic boundary conditions
• Fidelity approach to quantum phase transitions: finite size scaling for quantum Ising model in a transverse field
• Breakdown of a perturbed Z_N topological phase
• Visualizing elusive phase transitions with geometric entanglement
• Multipartite Entanglement Measures and Quantum Criticality from Matrix and Tensor Product States
• Topological transitions from multipartite entanglement with tensor networks: a procedure for sharper and faster characterization
• Assessing the accuracy of projected entangled-pair states on infinite lattices
• Finite-Size Geometric Entanglement from Tensor Network Algorithms
• Spontaneous symmetry breaking and bifurcations in ground state fidelity for quantum lattice systems
• Quantum phase transitions in a two-dimensional quantum XYX model: Ground-state fidelity and entanglement
• Plaquette Renormalization Scheme for Tensor Network States
• Geometric entanglement of critical XXZ and Ising chains and Affleck-Ludwig boundary entropies
• Phase diagram of the SO(n) bilinear-biquadratic chain from many-body entanglement
• Degenerate groundstates and multiple bifurcations in a two-dimensional q-state quantum Potts model
• Quantum phase transition in the $Z_3$ Kitaev-Potts model
• Geometric entanglement from matrix product state representations

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