# Multipartite entanglement measures and quantum criticality from matrix and tensor product states

@article{Huang2010MultipartiteEM, title={Multipartite entanglement measures and quantum criticality from matrix and tensor product states}, author={Ching-Yu Huang and Feng-Li Lin}, journal={Physical Review A}, year={2010}, volume={81}, pages={032304} }

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 and TPSs). We use the infinite time-evolving block decimation (iTEBD) method to find the ground states numerically in the form of MPSs and TPSs, and then evaluate their entanglement measures by the method of tensor renormalization group (TRG). We find that these entanglement…

## Figures from this paper

## 30 Citations

Bipartite entanglement of the one-dimensional extended quantum compass model in a transverse field

- Physics
- 2012

By using the infinite time-evolving block decimation (iTEBD) method, we obtain the ground state wave function of the one-dimensional quantum compass model in a transverse field in the form of a…

Tensor-network approach to compute genuine multisite entanglement in infinite quantum spin chains

- PhysicsPhysical Review A
- 2019

We devise a method based on the tensor-network formalism to calculate genuine multisite entanglement in ground states of infinite spin chains containing spin-1/2 or spin-1 quantum particles. The…

Matrix product state, quantum entanglement, and criticality in the one-dimensional dimerized antiferromagnetic Heisenberg model

- Physics
- 2012

The matrix product state (MPS) is utilized to investigate the ground state properties and quantum phase transitions (QPTs) of the dimerized antiferromagnetic Heisenberg (DAH) model. The ground state…

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

- Physics
- 2015

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…

Matrix product state and quantum phase transitions in the one-dimensional extended quantum compass model

- Physics
- 2012

The matrix product state (MPS) is utilized to study the ground state properties and quantum phase transitions (QPTs) of the one-dimensional quantum compass model (QCM). The MPS wavefunctions are…

Geometric entanglement from matrix product state representations

- Physics
- 2011

An efficient scheme for computing the geometric entanglement (GE) per lattice site for quantum many-body systems on a periodic finite-size chain is proposed in the context of a tensor network…

Geometric entanglement for quantum critical spin chains belonging to the Ising and three-state Potts universality classes

- Physics
- 2012

Abstract The leading finite-size correction to the geometric entanglement per lattice site is investigated for the antiferromagnetic–ferromagnetic alternating Heisenberg model, quantum three-state…

Entanglement Entropy and Quantum Phase Transition in the O(N) σ-model

- PhysicsJournal of High Energy Physics
- 2021

Abstract
We investigate how entanglement entropy behaves in a non-conformal scalar field system with a quantum phase transition, by the replica method. We study the σ-model in 3+1 dimensions which…

Quantum entanglement and quantum phase transition for the Ising model on a two-dimension square lattice

- Physics
- 2016

The quantum entanglement and quantum phase transition of the transverse-field Ising model on a two-dimensional square lattice were investigated by applying the quantum renormalization group method.…

Quantum entanglement and quantum phase transition of the spin-1 Heisenberg chain with single-ion anisotropy

- Physics
- 2020

Quantum entanglement and quantum phase transition of the spin-1 Heisenberg chain with single-ion anisotropy have been investigated by using the quantum renormalization group method. It is found that…

## References

SHOWING 1-10 OF 74 REFERENCES

Entanglement and factorized ground states in two-dimensional quantum antiferromagnets.

- Physics, MedicinePhysical review letters
- 2005

It is shown that the ground state of anisotropic two-dimensional S=1/2 antiferromagnets in a uniform field takes the classical-like form of a product state for a particular value and orientation of the field, at which the purely quantum correlations due to entanglement disappear.

Quantum phase transitions in a two-dimensional quantum XYX model: ground-state fidelity and entanglement.

- Physics, MedicinePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2009

The fidelity per lattice site is computed to demonstrate that the field-induced quantum phase transition is unambiguously characterized by a pinch point on the fidelity surface, marking a continuous phase transition.

Universal geometric entanglement close to quantum phase transitions.

- Medicine, PhysicsPhysical review letters
- 2008

First analytical and general proofs that, for translationally invariant quantum systems in one spatial dimension, the global geometric entanglement per region of size L>>xi diverges with the correlation length as (c/12)log(xi/epsilon) close to a quantum critical point with central charge c, where is a cutoff at short distances.

Theory of finite-entanglement scaling at one-dimensional quantum critical points.

- Physics, MedicinePhysical review letters
- 2009

A quantitative theory of previously observed scaling behavior resulting from finite entanglement at quantum criticality is given, which is checked against numerical scaling at several quantum critical points.

Entanglement renormalization.

- Physics, MedicinePhysical review letters
- 2007

Numerical simulations with the ground state of a 1D lattice at criticality show that the resulting coarse-grained sites require a Hilbert space dimension that does not grow with successive RG transformations, and calculations unveil that ground state entanglement in extended quantum systems is organized in layers corresponding to different length scales.

Entanglement in quantum critical phenomena.

- Physics, MedicinePhysical review letters
- 2003

The results establish a precise connection between concepts of quantum information, condensed matter physics, and quantum field theory, by showing that the behavior of critical entanglement in spin systems is analogous to that of entropy in conformal field theories.

Global entanglement and quantum criticality in spin chains

- Physics
- 2005

The entanglement of quantum $XY$ spin chains of arbitrary length is investigated via a recently developed global measure suitable for generic quantum many-body systems. This entanglement is…

A short review on entanglement in quantum spin systems

- Physics
- 2009

We review some of the recent progress on the study of entropy of entanglement in many-body quantum systems. Emphasis is placed on the scaling properties of entropy for one-dimensional multi-partite…

Tensor-entanglement renormalization group approach as a unified method for symmetry breaking and topological phase transitions

- Physics
- 2008

Traditional mean-field theory is a generic variational approach for analyzing symmetry breaking phases. However, this simple approach only applies to symmetry breaking states with short-range…

Geometric measure of entanglement and applications to bipartite and multipartite quantum states

- Physics
- 2003

The degree to which a pure quantum state is entangled can be characterized by the distance or angle to the nearest unentangled state. This geometric measure of entanglement, already present in a…