Canonically transformed wavefunctions and operators for the ground state of the Hubbard model

Michele Cini, Gianluca Stefanucci, A. Balzarotti

Pongpun Punpet, Chatchai Srinitiwarawong

The ground-state properties of a simple model for transition metal oxide compounds in ferromagnetic phase have been studied. This model only contains the orbital degree of freedom. The two-orbital spinless Hubbard model in the limit of strong on-site coulomb interaction (U) has been used to describe the motion of election in e[subscript g] orbital. In the large-U and half-filling limits, the effective Hamilto-nian has been derived from the Hubbard model by the canonical transformation. After the transformation, the doubly occupied states have been projected out and the size of the Hillbert space has been reduced. For this effective Hamiltonian, the hopping amplitudes have been defined according to the managanite system which consists of three axes: x-, y- and z-axis. Since the ground-state properties of the effective Hamiltonian have been calculated only in one-dimension, then the results of this work have been separated in three cases; the electrons hopping in x, y, and z axes respectively. The ground-state wavefunction of this effective Hamiltionian has been calculated by infinite density matrix renormalization group algorithm. This algorithm leads to the ground state at the thermodynamic limit when the number of sties is large. It has been found that the ground-state energies are equivalent in all hopping axes. Furthermore, the nearest neighbor orbital correlations at the ground state for all axes are antiferro-orbital.

Tomotoshi Nishino

Yoshihiro Asai

Balázs Hetényi, Hans Gerd Evertz

The $t\ensuremath{-}J$ and Heisenberg models are truncated expansions of a canonically transformed Hubbard model coinciding with it at $U\ensuremath{\rightarrow}\ensuremath{\infty}$. We show that a modified canonical transformation applied to the Hubbard model leads to alternative models of similar form but whose convergence properties with respect to the expansion are more favorable, resulting in a good description of the half-filled ground state even at $0<U\ensuremath{\le}1$. We investigate the transformed Hamiltonian and observables for metallic and insulating variational wave functions.

J. M. P. Carmelo, R. Micnas

A variational wave function to describe the ground-state properties of the attractive Hubbard model is presented. The function is complementary to the Gutzwiller wave function for positive U. The results are in agreement with the canonical transformation which is known to relate the attractive and repulsive Hubbard models for all electronic densities.