Quantum Phase Transition and Entanglement in Topological Quantum Wires

Abstract

We investigate the quantum phase transition of the Su-Schrieffer-Heeger (SSH) model by inspecting the two-site entanglements in the ground state. It is shown that the topological phase transition of the SSH model is signified by a nonanalyticity of local entanglement, which becomes discontinuous for finite even system sizes, and that this nonanalyticity has a topological origin. Such a peculiar singularity has a universal nature in one-dimensional topological phase transitions of noninteracting fermions. We make this clearer by pointing out that an analogous quantity in the Kitaev chain exhibiting the identical nonanalyticity is the local electron density. As a byproduct, we show that there exists a different type of phase transition, whereby the pattern of the two-site entanglements undergoes a sudden change. This transition is characterised solely by quantum information theory and does not accompany the closure of the spectral gap. We analyse the scaling behaviours of the entanglement in the vicinities of the transition points.

References in corpus (23)

• Topological Insulators
• Quantum entanglement
• Unpaired Majorana fermions in quantum wires
• Separability of Mixed States: Necessary and Sufficient Conditions
• Three qubits can be entangled in two inequivalent ways
• Classification of topological insulators and superconductors in three spatial dimensions
• New directions in the pursuit of Majorana fermions in solid state systems
• Entanglement in quantum critical phenomena
• Topological entanglement entropy
• Detecting topological order in a ground state wave function
• Persistent entanglement in arrays of interacting particles
• 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 in a simple quantum phase transition
• Sudden Death of Entanglement
• Direct Measurement of the Zak phase in Topological Bloch Bands
• A Mott insulator of fermionic atoms in an optical lattice
• Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order
• Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order
• Bell Inequalities and the Separability Criterion
• Entanglement spectrum of topological insulators and superconductors
• Entangled graphs: Bipartite entanglement in multi-qubit systems
• Compressibility as a probe of quantum phase transitions in topological superconductors

Cited by in corpus (18)

• Magnetic field induced quantum phases in a tensor network study of Kitaev magnets
• Unifying topological phase transitions in noninteracting, interacting, and periodically driven systems
• Many-body entanglement in a topological chiral ladder
• Phase transitions of the anisotropic Dicke model
• Quantum correlations and entanglement in a Kitaev-type spin chain
• Detecting topological phase transitions through entanglement between disconnected partitions in a Kitaev chain with long-range interactions
• Global entanglement in a topological quantum phase transition
• Characteristic length scales from entanglement dynamics in electric-field-driven tight-binding chains
• Topological phase transiton of anisotropic XY model with Dzyaloshinskii-Moriya interaction
• Entanglement spectrum and entropy in Floquet topological matter
• Quantum probing topological phase transitions by non-Markovianity
• Tunable mode entanglement: topological Su-Schrieffer-Heeger (SSH) chain with an embedded Aharonov-Bohm quantum ring
• Quantum entanglement and transport in non-equilibrium interacting double-dot setup: The curious role of degeneracy
• Genuine tripartite entanglement as a probe of quantum phase transitions in a spin-1 Heisenberg chain with single-ion anisotropy
• Interaction-driven phase transition in one dimensional mirror-symmetry protected topological insulator
• Extended edge modes and disorder preservation of a symmetry-protected topological phase out of equilibrium
• Entanglement signatures of a percolating quantum system
• Temporal Entanglement Transitions in the Periodically Driven Ising Chain