Abstract
We present a generic framework for the emergence of the {{mathbb{Z}}}_{2} toric-code and the double-semion topological order in a wide class of hardcore Bose-Hubbard-type models governed by density-density interaction and in the strong-interaction regime. We fix fractional filling factor and study under which conditions the density-density interaction gives rise to topological degeneracy. We further specify which dynamics determines the toric-code and the double-semion topological order. Our results indicate that the specifics of the density-density interaction determine the long-range entanglement of the model which possesses “restricted patterns” of the long-range entanglement realized in corresponding string-net models with the same topological order.
Highlights
Hardcore lattice bosons (HLB) in two spatial dimensions form a wide class of strongly correlated many-body systems which includes models realizable experimentally with cold atoms and molecules trapped in optical lattices
HLB are described by Bose-Hubbard-type models where the correlation is governed by a two-site density-density interaction which is diagonal in the Fock basis and expressed as a sum of local operators, H0 = ∑i,j Vijninj
Given the long-range-entanglement “pattern” in ground states of certain string-net models, we argue, under certain conditions, the existence of the same topological order in strong-interaction Bose-Hubbard-type lattice models through
Summary
Hardcore lattice bosons (HLB) in two spatial dimensions form a wide class of strongly correlated many-body systems which includes models realizable experimentally with cold atoms and molecules trapped in optical lattices. It has been reported that for certain lattice geometries, certain Vij’s, and appropriate fixed filling factor, strongly interacting HLB harbor 2 topological order and form gapped quantum spin liquid[1,2,3,4,5] These observations prompted considerable interest in exploring strongly interacting lattice models which harbor topological order and have the potential to be experimentally realized[11, 13, 14]. They specify which dynamics leaves 0 invariant, or equivalently, stipulate how the position of bosons in a given Fock state in 0 can be moved generating another Fock state in 0 As it will become clear in the following discussion, the “local constraints” determine the capability of strongly-interacting HLB to harbor TC topological order and DS topological order. Throughout this paper, by topologically ordered phase in the strong-interaction limit, we mean a gapped phase (with a spectral gap and a finite ground-state degeneracy), extending upon approaching the limit of no dynamics, which has nontrivial bulk topological degeneracy and locally indistinguishable ground states
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