Numerical Study Of The Dynamic Hubbard Model

Using constrained-path Monte Carlo method (CPMC) and exact diagonalization (ED) technique, we studied the three-band and one-band dynamic Hubbard model. The dynamic Hubbard model was firstly introduced by J. E. Hirsch, which considers a wide spread phenomenon that when an electron is added to an already occupied electronic orbital, the orbital will expand itself because of the strong repulsive Coulomb interaction between electrons. This kind of phenomenon can be taken into consideration by introducing an auxiliary spin field coupled to the double occupancy.We first discuss the development of CPMC for the dynamic Hubbard model and analyze the error of CPMC when it is applied to simulate the properties of the small lattice compared to the results from ED. In the one-band dynamic Hubbard model, we compare the results of kinetic energy and the magnetic moment of the Cu atoms from CPMC and ED. We find that the CPMC simulation can reflect the tendency of kinetic energy and magnetic moment when changing the coupling strength of the auxiliary spin field (ASF) and the on-site interaction of the Cu atoms. In the three-band model we find that in the small charge-transfer energy region, the CPMC simulation agrees well the ED results; in the normal charge transfer energy region, however, the error of CPMC starts to increase. In order to obtain reliable results, in our later CPMC simulation, we will choose the small charge transfer energy.In the three-band dynamic Hubbard model, we find that the hole-binding energy is suppressed by the ASF. An analysis of the contribution of different energies to the binding energy shows an ASF-induced lowering of the kinetic energy, signaling a possible kinetic-energy-driven pairing mechanism. The suppression of hole-binding energy, together with the ASF-induced reduction of spectral weight, leads to a decrease of the long-range part of d-wave pairing correlations. Contrary to previous quantum Monte Carlo study of the dynamic Hubbard model, we find that d-wave symmetry, instead of the extended s-wave symmetry, is dominant in the three-band model. In the one-band model, the ED simulation also shows a suppression of the hole-binding energy and reduction of spectral weight when we turn on the coupling of the ASF. However, the CPMC simulation shows that the long-range part of d-wave pairing correlations is increased because of the ASF. The disagreement of the two numerical techniques on this point is still one of our research problems.