# Quantum phases of tilted dipolar bosons in two-dimensional optical lattice

## TL;DR

This paper investigates the quantum phases of tilted dipolar bosons in 2D optical lattices, revealing various ordered phases and phase transitions influenced by tilt angle, using Gutzwiller mean-field theory and perturbation analysis.

## Contribution

It introduces a minimal extended Bose-Hubbard model to analyze tilt-angle-dependent quantum phases of dipolar bosons in 2D lattices, combining analytical and numerical methods.

## Key findings

- Checkerboard and striped phases depend on tilt angle.
- Intermediate phase is an emulsion or superfluid.
- System becomes unstable and collapses at high tilt angles.

## Abstract

We consider a minimal model to describe the quantum phases of ultracold dipolar bosons in two-dimensional (2D) square optical lattices. The model is a variation of the extended Bose-Hubbard model and apt to study the quantum phases arising from the variation in the tilt angle $\theta$ of the dipolar bosons. At low tilt angles $0^{\circ}\leqslant\theta\apprle25^{\circ}$, the ground state of the system are phases with checkerboard order, which could be either checkerboard supersolid or checkerboard density wave. For high tilt angles $55^{\circ}\apprge\theta\apprge35^{\circ}$, phases with striped order of supersolid or density wave are preferred. In the intermediate domain $25^{\circ}\apprle\theta\apprle35^{\circ}$ an emulsion or SF phase intervenes the transition between the checkerboard and striped phases. The attractive interaction dominates for $\theta\apprge55^{\circ}$, which renders the system unstable and there is a density collapse. For our studies we use Gutzwiller mean-field theory to obtain the quantum phases and the phase boundaries. In addition, we calculate the phase boundaries between an incompressible and a compressible phase of the system by considering second order perturbation analysis of the mean-field theory. The analytical results, where applicable, are in excellent agreement with the numerical results.