2002/07/24 by N. G. Zhang, Zhang, N. G., C. L. Henley +2
Physics and Astronomy · #Advanced Condensed Matter Physics #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Physics of Superconductivity and Magnetism #Strongly Correlated Electrons (cond-mat.str-el) #cond-mat.str-el
paper · pdf · doi:10.48550/arxiv.cond-mat/0207571
25 pages, 18 figures
arxiv created 2002/07/24 · openalex publication_date 2002/07/24 · arxiv updated 2009/11/30 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
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.