Phase diagram and sweep dynamics of a one-dimensional generalized cluster model

Abstract

We numerically study quantum phase transitions and dynamical properties in the one-dimensional cluster model with several interactions by using the time-evolving block decimation method for infinite systems and the exact diagonalization. First, boundaries among several quantum phases of the model are determined from energy gap and each phase is characterized by order parameters and the entanglement spectrum (ES). We confirm that in the model with open boundary condition the degeneracy of the lowest levels in the ES corresponds to that of the ground states. Then, using the time-dependent Bogoliubov transformation with open boundary condition, we investigate dynamical properties during an interaction sweep through the critical point which separates two topological phases involving four-fold degeneracy in the ground state. After a slow sweep across the critical point, we observe spatially periodic structures in the string correlation functions and the entanglement entropy. It is shown that the periodicities stem from the Bogoliubov quasiparticles generated near the critical point.

arXiv comment5 pages, 3 figures

References in corpus (37)

• Unpaired Majorana fermions in quantum wires
• Nonequilibrium dynamics of closed interacting quantum systems
• Topological entanglement entropy
• Detecting topological order in a ground state wave function
• 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
• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• Topological phases of fermions in one dimension
• Dynamics of a Quantum Phase Transition
• Dynamics of a Quantum Phase Transition and Relaxation to a Steady State
• Identifying Topological Order by Entanglement Entropy
• The iTEBD algorithm beyond unitary evolution
• General Relationship Between the Entanglement Spectrum and the Edge State Spectrum of Topological Quantum States
• Entanglement spectrum and boundary theories with projected entangled-pair states
• Three-spin interactions in optical lattices and criticality in cluster Hamiltonians
• Characterizing topological order by studying the ground states of an infinite cylinder
• Majorana zero modes in a quantum Ising chain with longer-ranged interactions
• Exotic Freezing of Response in Quantum Many-Body System
• Quenching Dynamics of a quantum XY spin-1/2 chain in presence of a transverse field
• 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
• Dynamics of entanglement entropy and entanglement spectrum crossing a quantum phase transition
• Entanglement spectrum of random-singlet quantum critical points
• Phase transitions and localizable entanglement in cluster-state spin chains with Ising couplings and local fields
• Phase diagram and quench dynamics of the Cluster-XY spin chain
• Symmetry-protected topological phases of alkaline-earth cold fermionic atoms in one dimension
• Dynamical delocalization of Majorana edge states by sweeping across a quantum critical point
• Entanglement Spectra of the 2D AKLT Model: VBS/CFT Correspondence
• Topological Blocking in Quantum Quench Dynamics
• Density-Matrix Renormalization Group Study of Extended Kitaev-Heisenberg Model
• Entanglement Spectra of the quantum hard-square model: Holographic minimal models
• Measurement-Based Quantum Computation on Symmetry Breaking Thermal States
• Hidden Order and Dynamics in Supersymmetric Valence Bond Solid States -- Super-Matrix Product State Formalism
• Topological Phase Transition in the Extended Cluster Compass Ladder
• Non-monotonic Dynamics in Frustrated Ising Model with Time-Dependent Transverse Field

Cited by in corpus (7)

• Infinite number of solvable generalizations of XY-chain, with cluster state, and with central charge c=m/2
• Topological and dynamical properties of a generalized cluster model in one dimension
• Zero modes of the Kitaev chain with phase-gradients and longer range couplings
• Exact solution of a cluster model with next-nearest-neighbor interaction
• Topological quantum phase transitions in a Majorana chain with spatial modulation
• Critical region of topological trivial and nontrivial phases in interacting Kitaev chain with spatially varying potentials
• Quantum correlations in a cluster spin model with three-spin interactions