Non-local correlations in the Haldane phase for an XXZ spin-1 chain: A perspective from infinite matrix product state representation

Abstract

String correlations are investigated in an infinite-size XXZ spin-1 chain. By using the infinite matrix product state representation, we calculate a long-range string order. In the XY phase, the string correlations decay within a relatively very large lattice distance, which makes a finite-size study difficult to verify the non-existence of the string order. Thus, in the Haldane phase, the non-vanishing string correlations in the limit of a very large distance allow to characterize the phase boundaries to the XY phase and the Neel phase, which implies that the transverse long-range string order is the order parameter for the Haldane phase. In addition, the singular behaviors of the von Neumann entropy and the fidelity per lattice site are shown to capture clearly the phase transition points that are consistent with the results from the string order. The estimated critical points including a BKT transition from the XY phase to the Haldane phase agree well with the previous results: ${\Delta }_{c2}=0$ for the XY-Haldane phase transition and ${\Delta }_{c3}=1.185$ for the Haldane-N'eel phase transition from the density renormalization group. From a finite-entanglement scaling of the von Neumann entropy with respect to the truncation dimension, the central charges are found to be $c\simeq 1.0$ at ${\Delta }_{c2}=0$ and $c\simeq 0.5$ at ${\Delta }_{c3}=1.185$, respectively, which shows that the XY-Haldane phase transition at ${\Delta }_{c2}=0$ belongs to the Heisenberg universality class, while the Haldane-Neel phase transition at ${\Delta }_{c2}=1.185$ belongs to the two-dimensional classical Ising universality class. It is also shown that, the long-range order parameters and the von Neumann entropy, as well as the fidelity per site approach, can be applied to characterize quantum phase transitions as a universal phase transition indicator for one-dimensional lattice many-body systems.

12 pages, 12 figures

References in corpus (44)

• Concentrating Partial Entanglement by Local Operations
• Entanglement in quantum critical phenomena
• Efficient classical simulation of slightly entangled quantum computations
• Scaling of Entanglement close to a Quantum Phase Transitions
• Entanglement in a simple quantum phase transition
• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• Ground state overlap and quantum phase transitions
• Universality of Entropy Scaling in 1D Gap-less Models
• Antiferromagnetic spin ladders: crossover between spin S = 1/2 and S = 1 chains
• Theory of finite-entanglement scaling at one-dimensional quantum critical points
• 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)
• Ground State Phase Diagram of S=1 XXZ Chains with Uniaxial Single-Ion-Type Anisotropy
• Rise and fall of hidden string order of lattice bosons
• Ground state fidelity from tensor network representations
• Physical Meaning of the Affleck-Kennedy-Lieb-Tasaki S=1 Quantum spin chain
• Quantum phase transitions in matrix product systems
• Equivalence of the antiferromagnetic Heisenberg ladder to a single $S=1$ chain
• Fidelity susceptibility and long-range correlation in the Kitaev honeycomb model
• Fidelity and Quantum phase transition for the Heisenberg chain with the next-nearest-neighbor interaction
• Quantum fidelity in the thermodynamic limit
• Phase Diagram of $S=1$ Bond-Alternating XXZ chains
• Ground State Phase Diagrams of Frustrated Spin-S XXZ Chains: Chiral Ordered Phases
• Theory of Chiral Order in Random Copolymers
• Quantum Entanglement in the Two Impurity Kondo Model
• Local Entanglement and quantum phase transition in spin models
• Phase diagram of the S=1/2 quantum spin chain with bond alternation
• Fragility of String Orders
• Operator fidelity susceptibility, decoherence and quantum criticality
• Fidelity, fidelity susceptibility and von Neumann entropy to characterize the phase diagram of an extended Harper model
• Investigation of Quantum Phase Transitions using Multi-target DMRG Methods
• Connectivity transition in the frustrated S=1 chain revisited
• Finite-size scaling of string order parameters characterizing the Haldane phase
• Spontaneous symmetry breaking and bifurcations in ground state fidelity for quantum lattice systems
• Local versus Nonlocal Order Parameter Field Theories for Quantum Phase Transitions
• Quantum phase transitions in three-leg spin tubes
• Fidelity susceptibility and general quench near an anisotropic quantum critical point
• Density-functional fidelity approach to quantum phase transitions
• Quantum phase transition in easy-axis antiferromagnetic Heisenberg spin-1 chain
• Disorder-induced phases in the S=1 antiferromagnetic Heisenberg chain
• Dimer and Néel order-parameter fluctuations in the spin-fluid phase of the s=1/2 spin chain with first and second neighbor couplings
• Ground state fidelity in bond-alternative Ising chains with Dzyaloshinskii-Moriya interactions
• Entanglement properties of quantum spin chains
• Phase diagram of S=1 XXZ chain with next-nearest neighbor interaction

Cited by in corpus (20)

• Quantum Correlations and Coherence in Spin-1 Heisenberg Chains
• Kaleidoscope of quantum phases in a long-range interacting spin-1 chain
• Dimensional enhancements in a quantum battery with imperfections
• Topological quantum phase transition in bond-alternating spin-1/2 Heisenberg chains
• Quantum coherence and spin nematic to nematic quantum phase transitions in biquadratic spin-1 and -2 XY chains with rhombic single-ion anisotropy
• Signatures of quantum phase transitions after quenches in quantum chaotic one-dimensional systems
• Finite-temperature fidelity and von Neumann entropy in the honeycomb spin lattice with quantum Ising interaction
• Quantum phase transitions in a spin-1 antiferromagnetic chain with long-range interactions and modulated single-ion anisotropy
• Quantum Fisher Information and multipartite entanglement in spin-1 chains
• Heisenberg and Dzyaloshinskii-Moriya interactions controlled by molecular packing in tri-nuclear organometallic clusters
• Non universality of entanglement convertibility
• Spin-1 Haldane phase in a chain of Rydberg atoms
• Spin dynamics of the anisotropic spin-1 antiferromagnetic chain at finite magnetic fields
• Entanglement entropy and massless phase in the antiferromagnetic three-state quantum chiral clock model
• Resilience of hidden order to symmetry-preserving disorder
• Quantum Simulation of Spin-1 XXZ-Heisenberg Models and the Haldane Phase with Dysprosium
• Bell-type correlation at quantum phase transitions in spin-1 chain
• Anomalous fractional quantization in the kagomelike Heisenberg ladder: Emergence of the effective spin-1 chain
• Critical exponents of block-block mutual information in one-dimensional infinite lattice systems
• Dynamical quantum phase transitions on random networks