Supersolidity in the one-dimensional Bose-Hubbard Model

We show how a variational Monte Carlo method can be constructed based on the Baeriswyl wavefunction to calculate the ground-state properties of one-dimensional Bose-Hubbard model. The phase diagram obtained is in excellent agreement with previous quantum Monte Carlo results. We also investigate the sensitivity of the system to a boundary twist, and find that it is sizeable even for integer fillings. To understand the nature of the phase we use a single-particle and a many-particle localization quantity and find that at integer fillings the system exhibits many-particle localization, at the same time, single particles as a result of bosonic exchange, can delocalize over the entire lattice. Away from integer fillings, where the system is known to be superfluid, delocalization is found at both the single-particle and many-particle level. We interpret these results as a signature of supersolidity in the Bose-Hubbard model at integer filling.