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Thermodynamics of a 4‐site Hubbard model by analytical diagonalization
Author(s) -
Schumann R.
Publication year - 2002
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/1521-3889(200201)11:1<49::aid-andp49>3.0.co;2-7
Subject(s) - hubbard model , physics , thermodynamic limit , eigenvalues and eigenvectors , canonical ensemble , grand canonical ensemble , electronic correlation , electron , magnetic field , partition function (quantum field theory) , perturbation theory (quantum mechanics) , quantum mechanics , condensed matter physics , statistics , superconductivity , mathematics , monte carlo method
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 susceptibility 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. For both the grand canonical and the canonical ensemble the high‐temperature crossing points of the specific heat are calculated. Whereas in the weak correlation regime the universal value calculated by second order perturbation theory for several Hubbard systems being in the thermodynamic limit is confirmed, these crossing points vanish for intermediate to strong correlation.