Unusual Finite-Temperature Phase Diagram for Semi-hard-core Bosons in Two Dimensions

Abstract

The extended bosonic Hubbard model (EBHM) is a paradigmatic model for the highly topical field of ultracold gases in optical lattices. Using quantum Monte Carlo simulations, we have determined the finite-temperature phase diagram of the EBHM with truncation of the on-site Hilbert space to the three lowest occupation states: n = 0, 1, 2 (semi-hard-core boson Hubbard model) given nearest-neighbor repulsion, however, both positive and negative values of the on-site boson–boson coupling U. This model is equivalent to an anisotropic spin-1 XXZ model ($n=S_z+1$) in a magnetic field. In the limit of large negative U (the boson–boson attraction), the model turns into the well-known model of hard-core bosons whose rich phase diagram demonstrates several puzzling features, in particular, signatures of an unusual reentrant behavior with a charge ordering upon increasing the temperature. We have shown that the rise of the correlation parameter U to positive values (the boson–boson repulsion) expectedly leads to a lowering of the temperature of the superfluid transition and unexpectedly to the more and more pronounced “reentrance” effect.