Bose-Hubbard model on a star lattice

TL;DR

This paper investigates the phase diagram of the Bose-Hubbard model on a star lattice, revealing unique Mott phases and quantum phase transitions using quantum Monte Carlo and dual vortex theory.

Contribution

It provides the first detailed analysis of the Bose-Hubbard model on a star lattice, identifying novel Mott phases and characterizing the nature of superfluid-insulator transitions.

Findings

Mott phases at 1/2 and 1/3 fillings are either RVB or coexisting density-wave and RVB phases.

Translationally invariant Mott states undergo second order superfluid-insulator transitions.

Transitions at the tip of the Mott lobe belong to the inverted XY universality class.

Abstract

We analyze the Bose-Hubbard model of hardcore bosons with nearest neighbor hopping and repulsive interactions on a star lattice using both quantum Monte Carlo simulation and dual vortex theory. We obtain the phase diagram of this model as a function of the chemical potential and the relative strength of hopping and interaction. In the strong interaction regime, we find that the Mott phases of the model at 1/2 and 1/3 fillings, in contrast to their counterparts on square, triangular, and Kagome lattices, are either translationally invariant resonant valence bond (RVB) phases with no density-wave order or have coexisting density-wave and RVB orders. We also find that upon increasing the relative strength of hopping and interaction, the translationally invariant Mott states undergo direct second order superfluid-insulator quantum phase transitions. We compute the critical exponents for these transitions and argue using the dual vortex picture that the transitions, when approached through the tip of the Mott lobe, belong to the inverted XY universality class.