Phase Transition in Fermion Lattice Gas with Infinite-Ranged Interaction. I: Ground State Properties

Abstract

The gas-liquid transition of quantum lattice gas model with infinite-ranged attractive interaction is studied in the case of spinless (or completely polarized) fermions. The Hamiltonian is given by where L and z denote the number of the lattice sites and the number of the nearest neighboring sites, respectively. This model corresponds to the quantized version of the classical Husimi-Temperley model and can be regarded as a lattice gas analog of the quantum van der Waals theory. Equation of state and phase diagram are calculated exactly at zero temperature. It is found that the transition behavior is quite sensitive to the shape of the density of states which depends on the dimensionality, the lattice structure and the form of the hopping. In most cases, the system shows the first-order gas-liquid transition for a suitable range of the parameters even at zero temperature (quantum condensation phenomena). In the case of linear chain with nearest neighbor hopping, the corresponding boson lattice gas and the spin 1/2 fermion lattice gas are also solved.