Phase diagrams of Bose-Hubbard model and Haldane-Bose-Hubbard model with complex hopping amplitudes

TL;DR

This paper investigates the phase diagrams of Bose-Hubbard models with complex hopping amplitudes on square and honeycomb lattices using quantum Monte Carlo simulations, revealing vortex-solid states, rich phases, and edge states.

Contribution

It introduces a detailed phase diagram analysis of Bose-Hubbard models with complex hopping, including vortex-solid states and edge phenomena, using extended quantum Monte Carlo methods.

Findings

Vortex-solid states form at specific magnetic flux quanta on square lattices.

The honeycomb lattice model exhibits a rich phase diagram with various phases.

Edge states appear in the honeycomb lattice model on cylindrical geometry.

Abstract

In this paper, we study Bose-Hubbard models on the square and honeycomb lattices with complex hopping amplitudes, which are feasible by recent experiments of cold atomic gases in optical lattices. To clarify phase diagrams, we use an extended quantum Monte-Carlo simulations (eQMC). For the system on the square lattice, the complex hopping is realized by an artificial magnetic field. We found that vortex-solid states form for certain set of magnetic field, i.e., the magnetic field with the flux quanta per plaquette $f=p/q$, where $p$ and $q$ are co-prime natural numbers. For the system on the honeycomb lattice, we add the next-nearest neighbor complex hopping. The model is a bosonic analog of the Haldane-Hubbard model. By means of the eQMC, we study the model with both weak and strong on-site repulsions. Numerical study shows that the model has a rich phase diagram. We also found that in the system defined on the honeycomb lattice of the cylinder geometry, an interesting edge state appears.