Strong-coupling expansions for the topologically inhomogeneous Bose-Hubbard model

Abstract

We consider a Bose-Hubbard model with an arbitrary hopping term and provide the boundary of the insulating phase thereof in terms of third-order strong coupling perturbative expansions for the ground state energy. In the general case two previously unreported terms occur, arising from triangular loops and hopping inhomogeneities, respectively. Quite interestingly the latter involves the entire spectrum of the hopping matrix rather than its maximal eigenpair, like the remaining perturbative terms. We also show that hopping inhomogeneities produce a first order correction in the local density of bosons. Our results apply to ultracold bosons trapped in confining potentials with arbitrary topology, including the realistic case of optical superlattices with uneven hopping amplitudes. Significant examples are provided. Furthermore, our results can be extented to magnetically tuned transitions in Josephson junction arrays.

arXiv comment5 pages, 2 figures,final version

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• Phase Diagram of the Bose-Hubbard Model with T_3 symmetry
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• Strong-coupling perturbation theory for the extended Bose-Hubbard model
• Quantum phase transitions of interacting bosons on hyperbolic lattices
• Quantum dynamics of bosons in a two-ring ladder: dynamical algebra, vortex-like excitations and currents
• Cell strong coupling perturbative approach to the phase diagram of ultracold bosons in optical superlattices
• Strong-coupling expansion for the two-species Bose-Hubbard model
• Topological polarons, quasiparticle invariants and their detection in 1D symmetry-protected phases
• Mean-field phase diagram for Bose-Hubbard Hamiltonians with random hopping
• Topology-induced confined superfluidity in inhomogeneous arrays
• Microcanonical entropy for classical systems
• Strong-coupling expansion for the spin-1 Bose-Hubbard model
• Bose-Einstein condensation in tight-binding bands
• Bose-Einstein condensation in exotic lattice geometries
• The ${\mathbb{Z}}_2$ toric-code and the double-semion topological order of hardcore Bose-Hubbard-type models in the strong-interaction limit
• Ground state of composite bosons in low-dimensional graphs
• Zero-temperature phase transitions in dilute bosonic superfluids on a lattice