Topological and dynamical properties of a generalized cluster model in one dimension

Abstract

We study the ground-state phase diagram and dynamics of the one-dimensional cluster model with several competing interactions. Paying particular attention to the relation between the entanglement spectrum (ES) and the bulk topological (winding) number, we first map out the ground-state phases of the model and determine the universality classes of the transitions from the exact solution. We then investigate the dynamical properties during interaction sweeps through the critical points of topological phase transitions. When the sweep speed is slow, the correlation functions and the entanglement entropy exhibit spatially periodic structures. On top of this, the levels in the ES oscillate temporally during the dynamics. By explicitly calculating the above quantities for excited states, we attribute these behaviors to the Bogoliubov quasiparticles generated near the critical points. We also show that the ES reflects the strength of the Majorana correlation even for the excited states.

arXiv comment16 pages, 13 figures

References in corpus (41)

• Unpaired Majorana fermions in quantum wires
• Entanglement Entropy and Quantum Field Theory
• Topological entanglement entropy
• Detecting topological order in a ground state wave function
• Geometric and Renormalized Entropy in Conformal Field Theory
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Measurement-based quantum computation with cluster states
• Entanglement spectrum of a topological phase in one dimension
• Calculation of reduced density matrices from correlation functions
• Topological phases of fermions in one dimension
• Reduced density matrices and entanglement entropy in free lattice models
• Quantum Annealing and Analog Quantum Computation
• Identifying Topological Order by Entanglement Entropy
• Entanglement spectrum and boundary theories with projected entangled-pair states
• Three-spin interactions in optical lattices and criticality in cluster Hamiltonians
• Dynamical quantum phase transitions in random spin chains
• Majorana zero modes in a quantum Ising chain with longer-ranged interactions
• Topology induced anomalous defect production by crossing a quantum critical point
• Adiabatic quantum dynamics of a random Ising chain across its quantum critical point
• Topological Entanglement Entropy in the Quantum Dimer Model on the Triangular Lattice
• Statistical mechanics of the Cluster-Ising model
• Quantum phase transition between cluster and antiferromagnetic states
• Dynamics of a quantum phase transition in the random Ising model
• Boundary Fidelity and Entanglement in the symmetry protected topological phase of the SSH model
• Dynamics of entanglement entropy and entanglement spectrum crossing a quantum phase transition
• Phase transitions and localizable entanglement in cluster-state spin chains with Ising couplings and local fields
• Dynamical delocalization of Majorana edge states by sweeping across a quantum critical point
• Exact Analysis of Entanglement in Gapped Quantum Spin Chains
• Dynamics of the entanglement spectrum in spin chains
• Quench dynamics and parity blocking in Majorana wires
• Entanglement in an SU(n) Valence-Bond-Solid State
• Entanglement Spectra of the 2D AKLT Model: VBS/CFT Correspondence
• Topological Blocking in Quantum Quench Dynamics
• Realizing all $so(N{)}_1$ quantum criticalities in symmetry protected cluster models
• Classification of Mixed State Topology in One Dimension
• Entanglement Spectra of the quantum hard-square model: Holographic minimal models
• Measurement-Based Quantum Computation on Symmetry Breaking Thermal States
• Out of equilibrium correlation functions of quantum anisotropic XY models: one-particle excitations
• Out-of-equilibrium dynamics and thermalization of string order
• Entanglement in valence-bond-solid states on symmetric graphs
• Phase diagram and sweep dynamics of a one-dimensional generalized cluster model

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• Skeleton of Matrix-Product-State-Solvable Models Connecting Topological Phases of Matter
• Infinite number of solvable generalizations of XY-chain, with cluster state, and with central charge c=m/2
• Zero modes of the Kitaev chain with phase-gradients and longer range couplings
• Scaling of geometric phase versus band structure in cluster-Ising models
• Exact solution of a cluster model with next-nearest-neighbor interaction
• Entanglement dynamics and phase transitions of the Floquet cluster spin chain
• Integrable spin chains and the Clifford group
• Quantum criticality in many-body parafermion chains
• Pivoting through the chiral-clock family
• Critical region of topological trivial and nontrivial phases in interacting Kitaev chain with spatially varying potentials
• Topological quantum phase transitions in a Majorana chain with spatial modulation
• Complete characterization of spin chains with two Ising symmetries
• Emergent gapless spiral phases and conformal Lifshitz criticality in the cluster Ising model with off-diagonal interactions
• Entanglement transition in a cluster spin chain coupled with free spins