Bell-type correlation at quantum phase transitions in spin-1 chain
arXiv:2010.09999 · doi:10.3390/e22111282
Abstract
For the identification of non-trivial quantum phase, we exploit a Bell-type correlation that is applied to the one-dimensional spin-1 XXZ chain. It is found that our generalization of bipartite Bell correlation can take a decomposed form of transverse spin correlation together with high-order terms. The formulation of density-matrix renormalisation group is utilized to obtain the ground state of a given Hamiltonian with non-trivial phase. Subsequently Bell-SLK-type generalized correlation is evaluated through the analysis of the matrix product state. Diverse classes of quantum phase transitions in the spin-1 model are identified precisely through the evaluation of the first and the second moments of the generalized Bell correlations. The role of high-order terms in the criticality has been identified and their physical implications for the quantum phase has been revealed.
arXiv comment10 pages, 12 figures
References in corpus (38)
- The density-matrix renormalization group in the age of matrix product states
- Area laws for the entanglement entropy - a review
- Entanglement in quantum critical phenomena
- Bell nonlocality
- Efficient classical simulation of slightly entangled quantum computations
- A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
- Scaling of Entanglement close to a Quantum Phase Transitions
- Entanglement in a simple quantum phase transition
- Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order
- Bell inequalities for arbitrarily high dimensional systems
- Classification of Gapped Symmetric Phases in 1D Spin Systems
- Symmetry protection of topological order in one-dimensional quantum spin systems
- Matrix product states represent ground states faithfully
- Efficient numerical simulations with Tensor Networks: Tensor Network Python (TeNPy)
- Complete classification of 1D gapped quantum phases in interacting spin systems
- Diverging Entanglement Length in Gapped Quantum Spin Systems
- Ground State Phase Diagram of S=1 XXZ Chains with Uniaxial Single-Ion-Type Anisotropy
- Localizable Entanglement
- Bell Correlations in a Bose-Einstein Condensate
- Detecting non-locality in multipartite quantum systems with two-body correlation functions
- Genuine quantum correlations in quantum many-body systems: a review of recent progress
- Quantum phase transitions in matrix product systems
- Quantum Correlations and Coherence in Spin-1 Heisenberg Chains
- The phase diagram of the anisotropic spin-2 XXZ model: an infinite system DMRG study
- Generic Bell inequalities for multipartite arbitrary dimensional systems
- Scaling Properties of Fidelity in Spin-one Anisotropic Model
- Phase Diagram of Bond-Alternating XXZ chains
- Bell inequalities and entanglement at quantum phase transition in the XXZ Model
- Nonlocality and entanglement in the XY model
- Accurate determination of the Gaussian transition in spin-1 chains with single-ion anisotropy
- Entanglement and nonlocality are inequivalent for any number of particles
- Quantum instability and edge entanglement in a quasi-long-range order
- Finite-size scaling of string order parameters characterizing the Haldane phase
- Non-local correlations in the Haldane phase for an XXZ spin-1 chain: A perspective from infinite matrix product state representation
- Nonviolation of Bell's Inequality in Translation Invariant Systems
- Bell correlations at Ising quantum critical points
- Quantum phases of dimerized and frustrated Heisenberg spin chains with s = 1/2, 1 and 3/2: an entanglement entropy and fidelity study
- Measurable criteria of generalized non-locality under the correlation symmetry