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Low Temperature Physics

Problem on a single hole in the two-dimensional Hubbard model with infinite repulsion

Yu. V. Mikhaǐlova

Published May 1, 1996• 0 citations
Publisher

Abstract

The energy spectrum and wave functions in the two-dimensional Hubbard model with infinite repulsion are studied for an N × N cluster in a system with a single hole and an inverted spin. The calculations are carried out for given values of the total quasimomentum α of the system. The system of four nonlinear algebraic equations defining the energy levels of the cluster is derived. The analysis is confined to the simplest case when αx = αy = α, α = (0, π).

DOI
10.1063/10.0033998

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The energy spectrum and wave functions in the two-dimensional Hubbard model with infinite repulsion are studied for an N × N cluster in a system with a single hole and an inverted spin. The calculations are carried out for given values of the total quasimomentum α of the system. The system of four nonlinear algebraic equations defining the energy levels of the cluster is derived. The analysis is confined to the simplest case when αx = αy = α, α = (0, π).
All the energy eigenvalues of the Hubbard model with infinite repulsion on 2×2×2 cubic lattice for different electron numbers N e are calculated numerically. For N e =4, 7 the ground state is completely ferromagnetic; namely, total spin S is N e /2. For N e =5, the total spin of the ground state is 3/2. For N e =2, 6, it is zero. For N e =1, 3, it is 1/2. Thermodynamic quantities such as entropy, susceptibility and specific heat are calculated with the method of canonical ensemble. There are two peaks in the specific heat curve for N e =4, 5, 6, 7, but only one peak for N e =1, 2, 3.
Using symmetry considerations and exact diagonalization techniques, we examine the quantum numbers of the states that define the antiferromagnetic and superconducting gaps in the multiple-particle spectrum of the repulsive and attractive two-dimensional Hubbard models. Studying the behavior of the lowest-energy levels as a function of the chemical potential, we analyze all possible dopings in 10- and 16-site clusters for many values of U/t. The possibility of superconductivity in the repulsive Hubbard and in the t-J models is discussed.
I present a scheme for performing weak-coupling expansions for the Hubbard model on square clusters near half-filling. Using this scheme the 6 × 6 cluster with 2, 3 and 4 holes is considered. I have calculated the ground-state quantum numbers for the 3- and 4-hole cases. In the 3-hole case I find a nonzero momentum near the (±π/2, ±π/2) points, while for the four-hole case the momentum is (0, 0). The calculation of low-lying excited states indicates the opening of a spin gap as one dopes away from half-filling.