# Phase diagrams of Bose-Hubbard model and antiferromagnetic spin-1/2 models on a honeycomb lattice

## TL;DR

This paper explores the phase diagrams of the hard-core Bose-Hubbard model on a honeycomb lattice, revealing various phases including antiferromagnetic, 120-degree order, and Bose metal states through Monte Carlo simulations.

## Contribution

It provides the first detailed phase diagram of the Bose-Hubbard model on a honeycomb lattice considering next-nearest neighbor hopping effects.

## Key findings

- Identification of antiferromagnetic and 120-degree order phases.
- Discovery of a Bose metal phase with no long-range order.
- Phase diagrams obtained via extended path-integral Monte Carlo simulations.

## Abstract

Motivated by the recent experimental realization of the Haldane model by ultracold fermions in an optical lattice, we investigate phase diagrams of the hard-core Bose-Hubbard model on a honeycomb lattice. This model is closely related with a spin-1/2 antiferromagnetic (AF) quantum spin model. Nearest-neighbor (NN) hopping amplitude is positive and it prefers an AF configurations of phases of Bose-Einstein condensates. On the other hand, an amplitude of the next-NN hopping depends on an angle variable as in the Haldane model. Phase diagrams are obtained by means of an extended path-integral Monte-Carlo simulations. Besides the AF state, a 120$^o$-order state, there appear other phases including a Bose metal in which no long-range orders exist.