Thermodynamics of a 4-site Hubbard model by analytical diagonalization

Abstract

By use of the conservation laws a four-site Hubbard model coupled to a particle bath within an external magnetic field in z-direction was diagonalized. The analytical dependence of both the eigenvalues and the eigenstates on the interaction strength, the chemical potential and magnetic field was calculated. It is demonstrated that the low temperature behaviour is determined by a delicate interplay between many-particle states differing in electron number and spin if the electron density is away from half-filling. The grand partition sum is calculated and the specific heat, the suszeptibility as well as various correlation functions and spectral functions are given in dependence of the interaction strength, the electron occupation and the applied magnetic field. Furthermore, for both the grand canonical and the canonical ensemble the so called crossing points of the suszeptibility are calculated. They confirm the universal value predicted by Vollhardt [1].