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

References in corpus (21)

• Robustness of coherence: An operational and observable measure of quantum coherence
• Observable measure of quantum coherence in finite dimensional systems
• Quantum discord and quantum phase transition in spin chains
• Diverging Entanglement Length in Gapped Quantum Spin Systems
• Extending Noether's theorem by quantifying the asymmetry of quantum states
• Robustness of asymmetry and coherence of quantum states
• The Fidelity and Trace Norm Distances for Quantifying Coherence
• Localizable Entanglement
• Implementation of Spin Hamiltonians in Optical Lattices
• Quantum coherence and uncertainty in the anisotropic XY chain
• Ground state fidelity from tensor network representations
• Entanglement and Quantum Phase Transition Revisited
• Fidelity and Quantum phase transition for the Heisenberg chain with the next-nearest-neighbor interaction
• Fidelity approach to quantum phase transitions: finite size scaling for quantum Ising model in a transverse field
• Factorization and Criticality in the Anisotropic XY Chain via Correlations
• Local Measures of Entanglement and Critical Exponents at Quantum Phase Transitions
• Critical Point Estimation and Long-Range Behavior in the One-Dimensional XY Model Using Thermal Quantum and Total Correlations
• Gap scaling at Berezinskii-Kosterlitz-Thouless quantum critical points in one-dimensional Hubbard and Heisenberg models
• The Wigner-Yanase information can increase under phase sensitive incoherent operations
• DMRG Simulation of the SU(3) AFM Heisenberg Model
• Nonclassicality and criticality in symmetry-protected magnetic phases

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