Bosonic integer quantum Hall effect as topological pumping

Abstract

Based on a quasi-one-dimensional limit of quantum Hall states on a thin torus, we construct a model of interaction-induced topological pumping which mimics the Hall response of the bosonic integer quantum Hall (BIQH) state. The quasi-one-dimensional counterpart of the BIQH state is identified as the Haldane phase composed of two-component bosons which form effective spin-$1$ degrees of freedom. An adiabatic change between the Haldane phase and trivial Mott insulators constitute {\it off-diagonal} topological pumping in which the translation of the lattice potential for one component induces a current in the other. The mechanism of this pumping is interpreted in terms of changes in polarizations between symmetry-protected quantized values.

10 pages, 5 figures. v2: comment on the case of arbitrary integer filling added, references added

References in corpus (23)

• Topological Field Theory of Time-Reversal Invariant Insulators
• Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
• Hidden order in 1D Bose insulators
• Rise and fall of hidden string order of lattice bosons
• Composite Fermion Theory for Bosonic Atoms in Optical Lattices
• Quantum Hall system in Tao-Thouless limit
• Half-Filled Lowest Landau Level on a Thin Torus
• Spin pumping and measurement of spin currents in optical superlattices
• Quantum Phase Transition between Integer Quantum Hall States of Bosons
• Symmetry protected Spin Quantum Hall phases in 2-Dimensions
• Topological Classification of Gapped Spin Chains :Quantized Berry Phase as a Local Order Parameter
• Realization of Fractional Chern Insulators in the Thin-Torus-Limit with Ultracold Bosons
• Flux insertion, entanglement, and quantized responses
• Quantized pumping and phase diagram topology of interacting bosons
• Fractional charge pumping of interacting bosons in one-dimensional superlattice
• Microscopic Realization of 2-Dimensional Bosonic Topological Insulators
• $U(1)\times U(1)$ Symmetry Protected Topological Order in Gutzwiller Wave Functions
• Topological Electromagnetic Responses of Bosonic Quantum Hall, Topological Insulator, and Chiral Semi-Metal phases in All Dimensions
• Devil's staircases in synthetic dimensions and gauge fields
• Anomalous charge pumping in a one-dimensional optical superlattice
• Spin-chain description of fractional quantum Hall states in the Jain series
• Emergent Fermi sea in a system of interacting bosons
• Spin chain description of rotating bosons at $\nu =1$

Cited by in corpus (14)

• Many-body topological invariants for fermionic short-range entangled topological phases protected by antiunitary symmetries
• Breakdown of topological Thouless pumping in the strongly interacting regime
• Inequivalent Berry phases for the bulk polarization
• Spatial-Translation-Induced Discrete Time Crystals
• Devil's staircases in synthetic dimensions and gauge fields
• Thouless pumping and trapping of two-component gap solitons
• Nature of continuous phase transitions in interacting topological insulators
• Quantum Hall phase diagram of two-component Bose gases: Intercomponent entanglement and pseudopotentials
• Filling constraints on translation invariant dipole conserving systems
• Topological pump and bulk-edge-correspondence in an extended Bose-Hubbard model
• Bulk-edge Correspondence in the Adiabatic Heuristic Principle
• Correlated Zak insulator in organic antiferromagnets
• Bosonic Halperin fractional quantum Hall effect at filling factor $\nu =2/5$
• Polarization-based indices in quantum many-body systems: validity and extension beyond one dimension