Gabriele Costa — University of Messina #
Extended Bose-Hubbard Model on Small Grids: Exact Diagonalization and Path-Integral Monte Carlo Studies  #
In the last decades, the development of  sophisticated cooling techniques has enabled the trapping of atomic gases in optical lattices, thus providing a suitable platform  for the
study of collective effects in many-body quantum systems.
To a very good approximation, the behavior of bosonic atoms on a lattice can be described by an extended Bose–Hubbard (EBH) Hamiltonian, providing a paradigm of the superfluid-insulator transition, which has been extensively studied in the past by theory and simulations. Less attention has been paid to the behavior of the model in truncated lattices, with or without periodic boundary conditions. In this contribution we focus on the hard-core limit of the extended Bose-Hubbard model on small square and triangular grids --- i.e., sections of the square and triangular lattices containing up to 13 sites. By mapping out the zero-temperature phase diagram through exact diagonalization, we find ground-state characteristics that are markedly different from those emerging in the thermodynamic limit.
The dichotomy between superfluid-like and insulating-like behavior is then investigated also in two-dimensional systems of a few interacting bosons in the continuum, subject to confining and optical-lattice potentials. Using path-integral Monte Carlo simulations, we compute kinetic and potential energies, as well as superfluid fraction and exchange-cycle statistics, finding hints of Bose-Hubbard behavior even in few-particle systems.