Phase Diagram of the Bose-Hubbard Model with T_3 symmetry

Abstract

In this paper we study the quantum phase transition between the insulating and the globally coherent superfluid phases in the Bose-Hubbard model with 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 T_3 structure. The zero-temperature critical point as a function of a magnetic field shows the characteristic "butterfly" form. At fully frustration the superfluid region is strongly suppressed. In addition, due to the existence of the Aharonov-Bohm cages at f=1/2, we find 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 T_3 lattice. We name this new phase the Aharonov-Bohm (AB) 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, is dictated by the particular topology of the T_3 lattice. The results presented in this paper 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)D XY model to corroborate the analytical calculations with a more accurate quantitative analysis. We finally discuss experimental realization of the T_3 lattice both with optical lattices and with Josephson junction arrays.

arXiv comment16 pages, 17 figures

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• Flat Bands and Ferrimagnetic Order in Electronically Correlated Dice-Lattice Ribbons
• Optical conductivity of semi-Dirac and pseudospin-1 models: Zitterbewegung approach
• Gap generation and flat band catalysis in dice model with local interaction
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• Strain-induced pseudo-magnetic field in $\alpha -{\mathcal{T}}_3$ lattice
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• Magnon-magnon interaction and magnon relaxation time in ferromagnetic Cr2Ge2Te6 monolayer
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• Electrical and thermal transport through $\alpha -T_3$ NIS junction
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• Zigzag dice lattice ribbons: Distinct edge morphologies and structure-spectrum correspondences
• Layer-by-layer assembly of multilayer optical lattices: Application to displaced dice lattice
• Emergent topology of flat bands in a twisted bilayer $\alpha$-$T_3$ lattice
• Current distribution and group velocities for electronic states on $\alpha -{\mathcal{T}}_3$ lattice ribbons in a magnetic field
• Topological Properties of Bilayer $\alpha -T_3$ Lattice Induced by Polarized Light
• Mott phases and quantum phase transitions of extended Bose-Hubbard models in 2+1 dimensions