Quantum Correlations and Coherence in Spin-1 Heisenberg Chains

Abstract

We explore quantum and classical correlations along with coherence in the ground states of spin-1 Heisenberg chains, namely the one-dimensional XXZ model and the one-dimensional bilinear biquadratic model, with the techniques of density matrix renormalization group theory. Exploiting the tools of quantum information theory, that is, by studying quantum discord, quantum mutual information and three recently introduced coherence measures in the reduced density matrix of two nearest neighbor spins in the bulk, we investigate the quantum phase transitions and special symmetry points in these models. We point out the relative strengths and weaknesses of correlation and coherence measures as figures of merit to witness the quantum phase transitions and symmetry points in the considered spin-1 Heisenberg chains. In particular, we demonstrate that as none of the studied measures can detect the infinite order Kosterlitz-Thouless transition in the XXZ model, they appear to be able to signal the existence of the same type of transition in the biliear biquadratic model. However, we argue that what is actually detected by the measures here is the SU(3) symmetry point of the model rather than the infinite order quantum phase transition. Moreover, we show in the XXZ model that examining even single site coherence can be sufficient to spotlight the second-order phase transition and the SU(2) symmetry point.

8 pages. 5 figures

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• Quantum-memory-assisted entropic uncertainty relations
• Towards resource theory of coherence in distributed scenarios
• Using and reusing coherence to realize quantum processes
• Steered quantum coherence as a signature of quantum phase transitions in spin chains
• Quantum coherence of planar spin models with Dzyaloshinsky-Moriya interaction
• Logarithmic coherence: Operational interpretation of ${\ell }_1$-norm coherence
• Basis-independent quantum coherence and its distribution
• Quantum coherence and spin nematic to nematic quantum phase transitions in biquadratic spin-1 and -2 XY chains with rhombic single-ion anisotropy
• Quantum correlations, entanglement spectrum and coherence of two-particle reduced density matrix in the Extended Hubbard Model
• Thermal production, protection and heat exchange of quantum coherences
• Finite-size scaling of coherence and steered coherence in the Lipkin-Meshkov-Glick model
• Quantum phase transitions in spin-1 XXZ chains with rhombic single-ion anisotropy
• Quantum coherence in a compass chain under an alternating magnetic field
• Intrinsic decoherence effects on correlated coherence and quantum discord in XXZ Heisenberg model
• Quantum coherence and speed limit in the mean-field Dicke model of superradiance
• Calculation of quantum discord in arbitrary dimensions, especially for X- and other specialized states
• Quantifying coherence in terms of the pure-state coherence
• Quantum phase transitions in a spin-1 antiferromagnetic chain with long-range interactions and modulated single-ion anisotropy
• Correlation-induced coherence and its use in detecting quantum phase transitions
• Coherence generating power of unitary transformations via probabilistic average
• Catalytic Transformations in Coherence Theory
• Quantum Information Resources in Spin-1 Heisenberg Dimer Systems
• Distribution of quantum coherence and quantum phase transition in the Ising system
• Characterizing coherence with quantum observables
• Detecting quantum critical points at finite temperature via quantum teleportation: further models
• Coherence-mixedness trade-offs
• Identifying quantum phase transitions via geometric measures of nonclassicality
• Detecting quantum critical points at finite temperature via quantum teleportation
• Relating relative Rényi entropies and Wigner-Yanase-Dyson skew information to generalized multiple quantum coherences
• Thermal effects on coherence and excitation transfer
• Magnetic phases of spin-1 lattice gases with random interactions
• Broadcasting of quantum correlations in qubit-qudit systems
• Linear mapping between magnetic susceptibility and entanglement in conventional and exotic one-dimensional superfluids
• Discrete and generalized phase space techniques in critical quantum spin chains
• Single-ion anisotropy effects on the critical behaviors of quantum entanglement and correlation in the spin-1 Heisenberg chain
• Finite temperature detection of quantum critical points: a comparative study
• Finite temperature detection of quantum critical points via internal quantum teleportation
• Embedded Quantum Correlations in thermalized quantum Rabi systems
• Quantum coherence assisted dynamical phase transition
• Frozen condition of quantum coherence
• Thermal coherence of the Heisenberg model with Dzyaloshinsky-Moriya interactions in an inhomogenous external field
• Quantum quench thermodynamics at high temperatures
• Quantum Statistical Complexity Measure as a Signalling of Correlation Transitions
• Bell-type correlation at quantum phase transitions in spin-1 chain
• Dynamics of quantum resources in regular and Majorana fermion systems
• Quantifying High-Order Interdependencies in Entangled Quantum States
• Coherence in quantum estimation
• Diagonal Entropy and Topological Phase Transitions in Extended Kitaev Chains
• Experimental quantification of quantum coherence for a set of quantum states
• Finding the ground states of symmetric infinite-dimensional Hamiltonians: explicit constrained optimizations of tensor networks
• State convertibility under genuinely incoherent operations
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• Probabilistic Coherence Transformation Under Strictly Incoherent Operation