Finite-Size Geometric Entanglement from Tensor Network Algorithms

Abstract

The global geometric entanglement is studied in the context of newly-developed tensor network algorithms for finite systems. For one-dimensional quantum spin systems it is found that, at criticality, the leading finite-size correction to the global geometric entanglement per site behaves as $b/n$, where $n$ is the size of the system and $b$ a given coefficient. Our conclusion is based on the computation of the geometric entanglement per spin for the quantum Ising model in a transverse magnetic field and for the spin-1/2 XXZ model. We also discuss the possibility of coefficient $b$ being universal.

5 pages, 2 figures, and 3 tables.

References in corpus (28)

• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• Ground state overlap and quantum phase transitions
• Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
• DMRG and periodic boundary conditions: a quantum information perspective
• Fidelity, dynamic structure factor, and susceptibility in critical phenomena
• Quantum critical scaling of the geometric tensors
• The iTEBD algorithm beyond unitary evolution
• Entanglement spectrum in one-dimensional systems
• Scaling of entanglement support for Matrix Product States
• Variational study of hard-core bosons in a 2-D optical lattice using Projected Entangled Pair States (PEPS)
• Fidelity susceptibility, scaling, and universality in quantum critical phenomena
• Equivalence of critical scaling laws for many-body entanglement in the Lipkin-Meshkov-Glick model
• Variational quantum Monte Carlo simulations with tensor-network states
• Quantum fidelity and quantum phase transitions in matrix product states
• Ground-state fidelity in one-dimensional gapless model
• Exploring frustrated spin-systems using Projected Entangled Pair States (PEPS)
• Strings, Projected Entangled Pair States, and variational Monte Carlo methods
• Entanglement and factorized ground states in two-dimensional quantum antiferromagnets
• Entanglement and boundary critical phenomena
• Universal geometric entanglement close to quantum phase transitions
• Scaling Properties of Fidelity in Spin-one Anisotropic Model
• First order phase transition in the anisotropic quantum orbital compass model
• Fidelity approach to quantum phase transitions: finite size scaling for quantum Ising model in a transverse field
• Ground-state properties of the attractive one-dimensional Bose-Hubbard model
• Ground state fidelity and quantum phase transitions in free Fermi systems
• Geometric Entanglement in a One-Dimensional Valence Bond Solid State
• Numerical study of the hard-core Bose-Hubbard Model on an Infinite Square Lattice
• Ground-state fidelity of Luttinger liquids: A wave functional approach

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• Characterizing Genuine Multisite Entanglement in Isotropic Spin Lattices
• Finite-temperature fidelity and von Neumann entropy in the honeycomb spin lattice with quantum Ising interaction
• Universal Boundary Entropies in Conformal Field Theory: A Quantum Monte Carlo Study
• Equilibrium and dynamical phase transitions in fully connected quantum Ising model: Approximate energy eigenstates and critical time
• Computable genuine multimode entanglement measure: Gaussian vs. non-Gaussian
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• Geometric entanglement of critical XXZ and Ising chains and Affleck-Ludwig boundary entropies
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• Phase diagram of the SO(n) bilinear-biquadratic chain from many-body entanglement
• Variational determination of multi-qubit geometrical entanglement in NISQ computers
• Geometric entanglement and quantum phase transitions in two-dimensional quantum lattice models
• One-shot conclusive multiport quantum dense coding capacities
• Enhancing robustness of multiparty quantum correlations using weak measurement
• Patterns of Genuine Multipartite Entanglement in Frustrated Quantum Spin Systems
• Shared Purity of Multipartite Quantum States
• Scaling of the Formation Probabilities and Universal Boundary Entropies in the Quantum XY Spin Chain
• Tensor-network approach to compute genuine multisite entanglement in infinite quantum spin chains
• 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
• Entanglement of weighted graphs uncovers transitions in variable-range interacting models
• Geometric Entanglement in Valance-Bond-Solid state