The supersolidity in a bosonic Lieb lattice

We investigate interacting bosons on a two-dimensional Lieb lattice, taking into account kinetic tunneling terms between the nearest-neighboring and next-nearest-neighboring sites. In the frame of a time-dependent variational Gutzwiller method, ground states of the Bose–Hubbard model are accessible site by site. As a consequence, we figure out an exotic type of supersolid phase which particularly features a dual construction, but in the absence of interactions among different lattice sites. This dual supersolid state could be further supported by solving the Bose–Hubbard model via an exact diagonalization method, and feasibly generalized to a limiting case of hardcore bosons. We also map out the phase diagram with the help of the time-dependent variational Gutzwiller method. And it manifests that the regime of dual supersolid state is dominant. • The Bose–Hubbard model on the Lieb lattice is studied. • We identify the dual supersolid without off-site interaction. • We map out the phase diagram of the bosonic Lieb lattice.