Derivation of Effective Hamiltonian and Energy Gap

Jan Peřina

Raymond Chan, M. Gulácsi

An effective Hamiltonian for the two-band Hubbard model was derived by a canonical transformation which was calculated and summed up to infinite order . The transformed Hamiltonian contains terms with strongly renormalized interaction energies. These new interaction energies show sign reversals as a function of the hopping integral in addition to a strong reduction in the charge-transfer gap and a significant increase in the attractive oxygen Hubbard term.

F. Palumbo

I determine the intrinsic Hamiltonian of the relative motion of the constituent fermions of bosonic composites in superfluid fermion systems, assuming the effective fermion-fermion potential to be a sum of separable terms. The derivation is based on an expansion that treats composites, quasiparticles, and their interactions on the same footing. The intrinsic Hamiltonian of the composites is expressed in terms of the solution of the gap equation and of the form factors of the potential. It has the Brillouin-Wigner form, namely it is Hermitian and energy-dependent. In such a context, a solid justification is given for discarding negative energies of the composites. As a check, I rederive the dispersion law of the Bogoliubov-Anderson mode and the spectrum of the Bardasis and Schrieffer Hamiltonian. The possible occurrence of gapped modes depending on the form of the fermion-fermion interaction is discussed. The intrinsic wave functions are derived explicitly in the long wave limit, while their full determination requires numerical calculations.

Hong-Yi Fan, Xubing Tang, Weijun Gui

By means of the 'invariant eigenoperator' method which originates from the Heisenberg equation of motion, we derive the energy-level gap of some dynamic Hamiltonians in quantum optics, including a generalized Jaynes–Cummings model.