Phase Diagram of the Bose-Hubbard Model with T_3 symmetry

TL;DR

This paper investigates the quantum phase transitions in the Bose-Hubbard model on the T_3 (dice) lattice, revealing a new Aharonov-Bohm insulator phase and analyzing the phase diagram with various analytical and numerical methods.

Contribution

It introduces the Aharonov-Bohm insulator phase in the T_3 lattice Bose-Hubbard model and provides a comprehensive phase diagram analysis using multiple techniques.

Findings

Identification of the AB insulator phase with zero superfluid stiffness

Superfluid region suppression at full frustration

Hierarchy of Mott insulating states dictated by lattice topology

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.