Phase diagram of the Bose-Hubbard model withT3symmetry

Abstract

We study the quantum phase transition between the insulating and the globally coherent superfluid phases in the Bose-Hubbard model with ${\mathcal{T}}_3$ structure, the “dice lattice.” Even in the absence of any frustration the superfluid phase is characterized by modulation of the order parameter on the different sublattices of the ${\mathcal{T}}_3$ structure. The zero-temperature critical point as a function of magnetic field shows the characteristic “butterfly” form. At full frustration the superfluid region is strongly suppressed. In addition, due to the existence of the Aharonov-Bohm cages at $f=1∕2$, we find some evidence for the existence of an intermediate insulating phase characterized by a zero superfluid stiffness but finite compressibility. In this intermediate phase bosons are localized due to the external frustration and the topology of the ${\mathcal{T}}_3$ lattice. We name this new phase the Aharonov-Bohm insulator. In the presence of charge frustration the phase diagram acquires the typical lobe structure. The form and hierarchy of the Mott insulating states with fractional fillings are dictated by the particular topology of the ${\mathcal{T}}_3$ lattice. The results presented were obtained by a variety of analytical methods: mean-field and variational techniques to approach the phase boundary from the superconducting side and a strongly coupled expansion appropriate for the Mott insulating region. In addition we performed quantum Monte Carlo simulations of the corresponding $(2+1)$-dimensional $XY$ model to corroborate the analytical calculations with a more accurate quantitative analysis. We finally discuss experimental realization of the ${\mathcal{T}}_3$ lattice both with optical lattices and with Josephson junction arrays.