# Two supersolid phases in hard-core extended Bose-Hubbard model

## TL;DR

This paper explores how next-nearest-neighbor tunneling influences the phase diagram of the extended Bose-Hubbard model, revealing two new supersolid phases with checkerboard order and a half supersolid phase under kinetic frustration.

## Contribution

It introduces the existence of two distinct supersolid phases and a half supersolid phase in the extended Bose-Hubbard model with nnn tunneling, using cluster mean-field theory.

## Key findings

- Two supersolid states with checkerboard structure are found.
- A half supersolid phase with both solid and unconventional superfluid orders is established.
- Phase transitions out of these supersolids are characterized.

## Abstract

The effect of the next-nearest-neighbor (nnn) tunneling on the hard-core extended Bose-Hubbard model on square lattices is investigated. By means of the cluster mean-field theory, the ground-state phase diagrams are determined. When a modest nnn tunneling is introduced, depending on its sign, two distinct supersolid states with checkerboard crystal structures are found away from half-filing. The characters of various phase transitions out of these two supersolid states are discussed. In particular, for the case with kinetic frustration, the existence of a half supersolid phase possessing both solid and unconventional superfluid orders is established. Our work hence sheds light on the search of this interesting supersolid phase in real ultracold lattice gases with frustrated tunnelings.