Dilute limit of a strongly-interacting model of spinless fermions and hardcore bosons on the square lattice

TL;DR

This paper investigates the dilute limit of a strongly-interacting lattice model of spinless fermions and hardcore bosons, combining analytical and numerical methods to understand two-particle interactions and energy behaviors.

Contribution

It provides the first systematic study of the t-matrix in a strongly-interacting lattice model, extending beyond previous Hubbard model analyses.

Findings

Interaction energy is well captured by pairwise terms.

Energy as a function of density fits Schick's analytical result for dilute hard disks.

The model allows exact diagonalization of larger systems than previous studies.

Abstract

In our model, spinless fermions (or hardcore bosons) on a square lattice hop to nearest neighbor sites, and also experience a hard-core repulsion at the nearest neighbor separation. This is the simplest model of correlated electrons and is more tractable for exact diagonalization than the Hubbard model. We study systematically the dilute limit of this model by a combination of analytical and several numerical approaches: the two-particle problem using lattice Green functions and the t-matrix, the few-fermion problem using a modified t-matrix (demonstrating that the interaction energy is well captured by pairwise terms), and for bosons the fitting of the energy as a function of density to Schick's analytical result for dilute hard disks. We present the first systematic study for a strongly-interacting lattice model of the t-matrix, which appears as the central object in older theories of the existence of a two-dimensional Fermi liquid for dilute fermions with strong interactions. For our model, we can (Lanczos) diagonalize the 7 by 7 system at all fillings and the 20 by 20 system with four particles, thus going far beyond previous diagonalization works on the Hubbard model.