Plateau transitions of spin pump and bulk-edge correspondence

Abstract

Sequential plateau transitions of quantum spin chains ($S$=1,3/2,2 and 3) are demonstrated by a spin pump using dimerization and staggered magnetic field as synthetic dimensions. The bulk is characterized by the Chern number associated with the boundary twist and the pump protocol as a time. It counts the number of critical points in the loop that is specified by the $Z_2$ Berry phases. With open boundary condition, discontinuity of the spin weighted center of mass due to emergent effective edge spins also characterizes the pump as the bulk edge correspondence. It requires extra level crossings in the pump as a super-selection rule that is consistent with the Valence Bond Solid (VBS) picture.

arXiv comment11 pages, 6 figures

References in corpus (48)

• Topological Photonics
• Chern Numbers in Discretized Brillouin Zone: Efficient Method of Computing (Spin) Hall Conductances
• Entanglement spectrum of a topological phase in one dimension
• Topological States and Adiabatic Pumping in Quasicrystals
• Topological Bands for Ultracold Atoms
• Symmetry protection of topological order in one-dimensional quantum spin systems
• A Thouless Quantum Pump with Ultracold Bosonic Atoms in an Optical Superlattice
• Topological Thouless Pumping of Ultracold Fermions
• Exploring 4D Quantum Hall Physics with a 2D Topological Charge Pump
• Efficient numerical simulations with Tensor Networks: Tensor Network Python (TeNPy)
• QuSpin: a Python Package for Dynamics and Exact Diagonalisation of Quantum Many Body Systems part I: spin chains
• Complete classification of 1D gapped quantum phases in interacting spin systems
• QuSpin: a Python Package for Dynamics and Exact Diagonalisation of Quantum Many Body Systems. Part II: bosons, fermions and higher spins
• Four-Dimensional Quantum Hall Effect with Ultracold Atoms
• Spin-exchange interactions of spin-one bosons in optical lattices: singlet, nematic and dimerized Phases
• Implementation of Spin Hamiltonians in Optical Lattices
• Topological charge pumping in a one-dimensional optical lattice
• Quantized Berry Phases as Local Order Parameters of Quantum Liquids
• Quantum Hall plateau transitions in disordered superconductors
• Order Parameter to Characterize Valence-Bond-Solid States in Quantum Spin Chains
• Spin pumping and measurement of spin currents in optical superlattices
• $Z_Q$ Topological Invariants for Polyacetylene, Kagome and Pyrochlore lattices
• A Characterization of Topological Insulators: Chern Numbers for a Ground State Multiplet
• Topological Classification of Gapped Spin Chains :Quantized Berry Phase as a Local Order Parameter
• Multi-particle Wannier states and Thouless pumping of interacting bosons
• Topological charge pumping in the interacting bosonic Rice-Mele model
• Reexamination of Finite-Lattice Extrapolation of Haldane Gaps
• Berry Phase in Quantum Field Theory: Diabolical Points and Boundary Phenomena
• Sum Rule of the Hall Conductance in Random Quantum Phase Transition
• Designing spin-1 lattice models using polar molecules
• Many-body Chern number without integration
• Exact Analysis of Entanglement in Gapped Quantum Spin Chains
• Breakdown of topological Thouless pumping in the strongly interacting regime
• Bulk-edge correspondence in topological pumping
• Quantum Hall plateau transition in graphene with spatially correlated random hopping
• Quantum Spin Pump in S=1/2 antiferromagnetic chains -Holonomy of phase operators in sine-Gordon theory-
• Topological charge pumping of bound bosonic pairs
• Quantized Berry Phases for a Local Characterization of Spin Liquids in Frustrated Spin Systems
• $Z_N$ Berry Phases in Symmetry Protected Topological Phases
• Interaction Induced Topological Charge Pump
• Degeneracy and Consistency Condition of Berry phases: Gap Closing under the Twist
• Finite-size corrections to quantized particle transport in topological charge pumps
• Topological nature of magnetization plateaus in periodically modulated quantum spin chains
• Various Topological Mott insulators in strongly-interacting boson system in one-dimensional superlattice
• Berry phase investigation of spin-S ladders
• Plateaux Transitions in the Pairing Model:Topology and Selection Rule
• Precise estimation of the S = 2 Haldane gap by numerical diagonalization
• Sequential quantum phase transitions in $J_1$-$J_2$ Heisenberg chains with integer spins ($S>1$): Quantized Berry phase and valence-bond solids

Cited by in corpus (5)

• Phonon-induced breakdown of Thouless pumping in the Rice-Mele-Holstein model
• Topological pump and bulk-edge-correspondence in an extended Bose-Hubbard model
• The Asymmetric Valence-Bond-Solid States in Quantum Spin Chains: The Difference Between Odd and Even Spins
• Topological pump of $SU(Q)$ quantum chain and Diophantine equation
• Bulk-edge Correspondence in the Adiabatic Heuristic Principle