Fractional Topological Phases in Generalized Hofstadter Bands with Arbitrary Chern Numbers

Abstract

We construct generalized Hofstadter models that possess "color-entangled" flat bands and study interacting many-body states in such bands. For a system with periodic boundary conditions and appropriate interactions, there exist gapped states at certain filling factors for which the ground-state degeneracy depends on the number of unit cells along one particular direction. This puzzling observation can be understood intuitively by mapping our model to a single-layer or a multilayer system for a given lattice configuration. We discuss the relation between these results and the previously proposed "topological nematic states," in which lattice dislocations have non-Abelian braiding statistics. Our study also provides a systematic way of stabilizing various fractional topological states in $C>1$ flat bands and provides some hints on how to realize such states in experiments.

5+5 pages, 4+3 figures

References in corpus (28)

• Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices
• High temperature fractional quantum Hall states
• Light-induced gauge fields for ultracold atoms
• Realizing the Harper Hamiltonian with Laser-Assisted Tunneling in Optical Lattices
• Fractional quantum Hall states at zero magnetic field
• Nearly-flat bands with nontrivial topology
• Fractional quantum Hall effect in the absence of Landau levels
• Topological Flat Band Models and Fractional Chern Insulators
• Time-reversal symmetry breaking in circuit-QED based photon lattices
• Exotic non-Abelian anyons from conventional fractional quantum Hall states
• Topologically Robust Transport of Photons in a Synthetic Gauge Field
• Genons, twist defects, and projective non-Abelian braiding statistics
• Fractionalizing Majorana fermions: non-abelian statistics on the edges of abelian quantum Hall states
• Superconducting Proximity Effect on the Edge of Fractional Topological Insulators
• Fractional Chern Insulators in Topological Flat bands with Higher Chern Number
• Topological flat band models with arbitrary Chern numbers
• Fractional topological superconductors with fractionalized Majorana fermions
• Fractional Quantum Hall Effect in Topological Flat Bands with Chern Number Two
• Bloch Model Wavefunctions and Pseudopotentials for All Fractional Chern Insulators
• Flat bands with higher Chern number in pyrochlore slabs
• Induced self-stabilization in fractional quantum Hall states of light
• Gauge-Fixed Wannier Wave-Functions for Fractional Topological Insulators
• Adiabatic continuation of Fractional Chern Insulators to Fractional Quantum Hall States
• Adiabatic continuity between Hofstadter and Chern insulator states
• Engineering three-body interaction and Pfaffian states in circuit QED systems
• Lattice construction of pseudopotential Hamiltonians for Fractional Chern Insulators
• From fractional Chern insulators to Abelian and non-Abelian fractional quantum Hall states: adiabatic continuity and orbital entanglement spectrum
• 3- and 4-body Interactions from 2-body interactions in Spin Models: A Route to Abelian and Non-Abelian Fractional Chern Insulators

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• Topology and Interactions in a Frustrated Slab: Tuning from Weyl Semimetals to C > 1 Fractional Chern Insulators
• A discretized Chern-Simons gauge theory on arbitrary graphs
• Bosonic integer quantum Hall effect in optical flux lattices
• Model Fractional Chern Insulators
• Stability, phase transitions, and numerical breakdown of fractional Chern insulators in higher Chern bands of the Hofstadter model
• Recent Developments in Fractional Chern Insulators
• Quantum geometry and stability of the fractional quantum Hall effect in the Hofstadter model
• Characterization of quasiholes in two-component fractional quantum Hall states and fractional Chern insulators in $|C|=2$ flat bands
• Topological phases of the dimerized Hofstadter butterfly
• Correlations and entanglement in flat band models with variable Chern numbers
• Topological characterization of hierarchical fractional quantum Hall effects in topological flat bands with SU($N$) symmetry
• A dark state of Chern bands: Designing flat bands with higher Chern number
• Quantum Hall phase diagram of two-component Bose gases: Intercomponent entanglement and pseudopotentials
• Inducing topological flat bands in bilayer graphene with electric and magnetic superlattices
• Fractional Chern insulator candidate in twisted bilayer checkboard lattice
• Halperin $(m^{\prime },m,n)$ fractional quantum Hall effect in topological flat bands
• Unconventional Fractional Phases in Multi-Band Vortexable Systems
• Bosonic Halperin fractional quantum Hall effect at filling factor $\nu =2/5$
• Three-component fractional quantum Hall effect in topological flat bands