The theory of the superconductivity mediated by kinematic and exchange interactions in t?J and two-band Hubbard models in a paramagnetic state is formulated. The Dyson equations for the matrix Green functions in terms of the Hubbard operators are obtained in the non-crossing approximation. To calculate superconducting T c a numerical solution of self-consistent Eliashberg equations is proposed.

A perturbation theory scheme in terms of electron hopping which is based on the Wick’s theorem for Hubbard operators is developed. Diagrammatic series contain single-site vertices connected by hopping lines and it is shown that for each vertice the problem splits into the subspaces with “vacuum states” determined by the diagonal Hubbard operators and only excitations around these “vacuum states...

Different realizations of the Hubbard operators in different Hilbert spaces give rise to various microscopic lattice electron models driven by strong correlations. In terms Gutzwiller projected operators, most familiar examples are t-J and BCS-Hubbard at coupling. We focus on spin-dopon representation operators. this case no double occupancy constraint (NDO) can be reexpressed as a Kondo intera...

A scheme is presented to decompose the exponential of a two-body operator in a discrete sum over exponentials of one-body operators. This discrete decomposition can be used instead of the Hubbard-Stratonovich transformation in auxiliary-field quantum Monte-Carlo methods. As an illustration, the decomposition is applied to the Hubbard model, where it is equivalent to the discrete Hubbard-Straton...

An exact boson mapping of the reduced BCS (equal strength) pairing Hamiltonian is considered. In the mapping, fermion pair operators are mapped exactly to the corresponding bosons. The image of the mapping results in a Bose-Hubbard model with level dependent hopping. Though the resultant Bose-Hubbard Hamiltonian is non-Hermitian, all eigenvalues are real when Uk/t < 1, where k is the total numb...

The Hubbard Hamiltonian and its variants/generalizations continue to dominate the theoretical modelling of important problems such as high temperature superconductivity. In this note we identify the set of relevant operators for the Hubbard Hamiltonian with a magnetic field term. Permanent address: Department of Physics, University of Peshawar, Peshawar, NWFP, Pakistan. Institute of Applied Phy...

The Kondo divergences owing to interaction of current carriers with local moments in highly correlated electron systems are considered within the Hubbard and s-d exchange models with infinitely strong onsite interaction, the many-electron Hubbard representation being used. The picture of density of states containing a peak at the Fermi level is obtained. Various forms of the self-consistent app...

We present an exact, unconstrained representation of the electron operators in terms of operators of opposite statistics. We propose a path–integral representation for the t-J model and introduce a parameter controlling the semiclassical behaviour. We extend the functional approach to the Hubbard model and show that the mean–field theory is equivalent to considering, at Hamiltonian level, the F...