Entanglement convertibility by sweeping through the quantum phases of the alternating bonds $XXZ$ chain

Abstract

We study the entanglement structure and the topological edge states of the ground state of the spin-1/2 XXZ model with bond alternation. We employ parity-density matrix renormalization group with periodic boundary conditions. The finite-size scaling of Rényi entropies $S_2$ and $S_{\infty }$ are used to construct the phase diagram of the system. The phase diagram displays three possible phases: Haldane type (an example of symmetry protected topological ordered phases), Classical Dimer and Néel phases, the latter bounded by two continuous quantum phase transitions. The entanglement and non-locality in the ground state are studied and quantified by the entanglement convertibility. We found that, at small spatial scales, the ground state is not convertible within the topological Haldane dimer phase. The phenomenology we observe can be described in terms of correlations between edge states. We found that the entanglement spectrum also exhibits a distinctive response in the topological phase: the effective rank of the reduced density matrix displays a specifically large "susceptibility" in the topological phase. These findings support the idea that although the topological order in the ground state cannot be detected by local inspection, the ground state response at local scale can tell the topological phases apart from the non-topological phases.

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References in corpus (51)

• Quantum entanglement
• Entanglement Entropy and Quantum Field Theory
• Concentrating Partial Entanglement by Local Operations
• Entanglement in quantum critical phenomena
• Scaling of Entanglement close to a Quantum Phase Transitions
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Entanglement spectrum of a topological phase in one dimension
• Symmetry protected topological orders and the group cohomology of their symmetry group
• Spin Liquid Ground State of the $S=1/2$ Kagome Heisenberg Model
• Controlling Spin Exchange Interactions of Ultracold Atoms in Optical Lattices
• Measuring entanglement entropy through the interference of quantum many-body twins
• Calculation of reduced density matrices from correlation functions
• Conditions for a class of entanglement transformations
• Direct estimations of linear and non-linear functionals of a quantum state
• Universal Quantum Estimator
• General Relationship Between the Entanglement Spectrum and the Edge State Spectrum of Topological Quantum States
• Universality of Entropy Scaling in 1D Gap-less Models
• Measuring entanglement entropy of a generic many-body system with a quantum switch
• Multipartite entanglement in spin chains
• Parity effects in the scaling of block entanglement in gapless spin chains
• Bulk-Edge Correspondence in the Entanglement Spectra
• Controlling Correlated Tunneling and Superexchange Interactions with AC-Driven Optical Lattices
• Entanglement Spectrum, Critical Exponents and Order Parameters in Quantum Spin Chains
• Quantum Simulation of Spin Models on an Arbitrary Lattice with Trapped Ions
• Statistical mechanics of the Cluster-Ising model
• Quantum phase transition between cluster and antiferromagnetic states
• Order Parameter to Characterize Valence-Bond-Solid States in Quantum Spin Chains
• Necessary and Sufficient Conditions for the Trumping Relation
• Catalytic Conversion Probabilities for Bipartite Pure States
• Scaling Properties of Fidelity in Spin-one Anisotropic Model
• Topological order in 1D Cluster state protected by symmetry
• Quantum phases with differing computational power
• An order parameter for impurity systems at quantum criticality
• Improving entanglement and thermodynamic Rényi entropy measurements in quantum Monte Carlo
• Edge-entanglement spectrum correspondence in a nonchiral topological phase and Kramers-Wannier duality
• A path integral Monte Carlo method for Rényi entanglement entropies
• Fidelity approach to Gaussian transitions
• Inequalities that Collectively Completely Characterize the Catalytic Majorization Relation
• Multipartite-entanglement monotones and polynomial invariants
• Parity quantum numbers in the Density Matrix Renormalization Group
• Entanglement Spectroscopy using Quantum Monte Carlo
• Local characterization of 1d topologically ordered states
• Entanglement Entropy in Extended Quantum Systems
• Local convertibility and the quantum simulation of edge states in many-body systems
• Local response of topological order to an external perturbation
• Numerical evidences of spin-1/2 chain approaching spin-1 chain
• Local convertibility of the ground state of the perturbed Toric code
• Quench Dynamics of Topological Maximally-Entangled States
• Non universality of entanglement convertibility
• Breakdown of local convertibility through Majorana modes in a quantum quench
• Phase diagram of quantum critical system via local convertibility of ground state

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