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A Study Of The Internal Energy And Magnetic Spin Susceptibility Of The 2-D Hubbard Model Representation Of High Temperature Superconductors Via An Exact-Approach

An exact approach is re-visited in performing a comparative analysis of the attractive and repulsive 2-D Hubbard model (AHM and RHM respectively) which is used in describing a simplified 2x1 (Cu-O-Cu) lattice (known to play significant role in HT c -superconductivity in cuprates) with the use of the MATLAB. The response of the temperature-dependent internal energy, E(kT), to the simultaneous variation of both the on-site interaction and the nearestneighbour hopping integral (U,t) shows that HT c -superconducting materials described by the AHM are not only more stable but sustain their stable state over a relatively wider temperature range. The spectrum of the magnetic spin susceptibility,x(T), reveal certain interesting character which are used to account for various observed phenomena in HT c -superconducting materials (like the coexistence of charge density wave (CDW) and spin density wave (SDW) in the semiconducting phase of Ba 1-x K x BiO 3 and BaPb x Bi 1-x O 3 . Furthermore, various correlations are suggested while the outer limits of the critical values of U for pair formation and associated spin gap, Up=-2eV for AHM and 3eV for RHM. Results obtained are also in strong agreement with results of QMC simulations for more realistic 3-band Hubbard model among others.