Properties of Bose gas in a lattice model (strong interaction)

Abstract

The doubts concerning validity of gas approximation for strong interaction (for example, hard spheres) are expressed. A contradictory example - a Bose system in a lattice model - is considered. Namely, the X-Y model for spin 1/2 is taken. A state with spins directed downwards is considered to be vacuum with respect to the particles. An inverse spin (+1/2) corresponds to a particle. There is an usual band spectrum (one band) for a single particle. A trial function is written for a multiple particle system. This function was shown to be a good one within a macroscopic limit, when the particle and lattice site numbers tend to infinity (the ratio of energy standard deviation to average energy tends to zero). A result within the gas limit (particle number is small compared with the lattice site number) is compared with that obtained via generally accepted approach.