Two-dimensional topological order of kinetically constrained quantum particles

TL;DR

This paper demonstrates that kinetically constrained quantum particles on a 2D lattice can exhibit topological order, with potential relevance to cold-atom systems and fractional quantum Hall states.

Contribution

It introduces a new class of kinetically constrained models that can host topological order, expanding the understanding of mechanisms behind fractional quantum Hall phenomena.

Findings

Numerical evidence of topological ground-state degeneracies

Quantization of topological invariants in the models

Topological order arising without traditional density interactions

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.