Two-dimensional topological order of kinetically constrained quantum particles

Abstract

We investigate how imposing kinetic restrictions on quantum particles that would otherwise hop freely on a two-dimensional lattice can lead to topologically ordered states. The kinetically constrained models introduced here are derived as a generalization of strongly interacting particle systems in which hoppings are given by flux-lattice Hamiltonians and may be relevant to optically driven cold-atom systems. After introducing a broad class of models, we focus on particular realizations and show numerically that they exhibit topological order, as witnessed by topological ground-state degeneracies and the quantization of corresponding invariants. These results demonstrate that the correlations responsible for fractional quantum Hall states in lattices can arise in models involving terms other than density-density interactions.

arXiv commentv2: additional references, minor changes in text; published version

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• Schrieffer-Wolff Transformation for Periodically Driven Systems: Strongly Correlated Systems with Artificial Gauge Fields
• Synthetic dimensions in the strong-coupling limit: supersolids and pair-superfluids
• Fractional Chern Insulators in Bands with Zero Berry Curvature
• Symmetry breaking and fermionic fractional Chern insulator in topologically trivial bands
• Supersymmetry and multicriticality in a ladder of constrained fermions