We investigate the ground-state and finite-temperature properties of the Bose-Hubbard model using the standard basis operator method applied to the equation of motion for Green's functions. We show that by introducing the self-consistent approach, the theory goes significantly beyond the mean-field approximation, allowing more-precise description of quantum and thermal fluctuations. For optical lattice systems with ultracold bosons, we find relevant quantitative agreement with numerical and experimental data. In particular, the presented method reveals the importance of thermal fluctuations in time-of-flight experiments. For the most reliable fitting of the visibility analytical curve to the experimental data, the value of temperature is determined and proximity to the quantum regime is discussed. The problem of identification of the superfluid--Mott-insulator phase boundary from time-of-flight experiments is also considered.

Ground-state and finite-temperature properties of correlated ultracold bosons on optical lattices

The Hamiltonian of the electron-phonon interaction is derived and applied to the description of disordered transition metal alloys. The coupled set of equations for the electron and phonon Green functions is derived with the help of the equation-of-motion technique. Neglecting the vertex corrections in the self-energy operators the closed self-consistent system of equations is obtained. The relevant configurational averaging is performed in the framework of the CPA. The electronic specific heat in the low-temperature limit is calculated.



[Russian Text Ignored]

Electron—Phonon Interaction in Disordered Transition Metal Alloys

The problem of calculating statistical tensors rho qn(I) for the nuclear-ordered state in enhanced compounds such as HoVO4, PrNi5 etc., is examined within the framework of both a simple effective-field model and more sophisticated many-body theories, such as the RPA. It is shown that for simple ferromagnets and the anti-ferromagnets, a result, originally due to Callen and Shtrikman (1965), can be used to show that there is a one-to-one relationship between the rho qn(I) calculated using many-body Green function theories and the simple effective-field model. In addition a new recursion relationship is derived, linking statistical tensors of differing rank. This relationship holds for a wide class of renormalised collective excitation theories and is far more convenient to use in practice than either the moment-generating function of Callen (1963) or the methods of Tahir-Kheli and ter Haar (1962). Using first-order perturbation theory it is also shown that the Callen and Shtrikman result breaks down in the presence of a small axially symmetric quadrupole interaction. Thus it is unlikely that a simple check on the accuracy of 'simple effective-field statistical tensors' can be devised in the spirit of the Callen and Shtrikman result. Some comments are also made concerning the nuclear statistical tensors used to describe the gamma -ray emission patterns from the enhanced nuclear magnet HoVO/sub /(Allsop et al.).

http://iopscience.iop.org/article/10.1088/0022-3719/19/4/015/pdf

Many-body statistical tensors for the nuclear-ordered state

We propose a new model of the spin-polarised charge transport in magnetic oxides. A formula for the electric current is derived within the framework of a Green function formalism [1,2]. The Green functions are constructed from two types of operators. The first are the standard-basis operators [3,4], defined in a basis of p(s) - d hybridised eigen-states of central ionic clusters [5]. These operators are used on equal footing with the fermion creation and annihilation operators, which are defined for the band states () of the metallic electrodes. The proposed model is extended by an interaction with an external magnetic field in a way, which enables calculations of magnetoresistance. Special emphasis is put on a coupling of the centre and the attached electrodes. The method is tested on nano-structures of the transition metal oxides such as some of the magnetic garnets and/or manganites. The process is mediated both by the hybridisation between the extended states of the electrodes and localised states of the centre, as well as by the hybridisation at the centre between the atomic p(s) states of the anions and the nd states of the transition metal.

A model of spin-polarised charge transport in magnetic oxides

Dynamic Properties of the Heisenberg Model with Crystal Field Anisotropy: T =∞ Limit

We propose a self-consistent many-body theory for the standard basis operator Green's functions and obtain an exact Dyson-type matrix equation for the interacting many-level systems. A zeroth order approximation, which neglects all the damping effects, is investigated in detail for the anisotropic Heisenberg model, the isotropic quadrupolar system and the Hubbard model. In the case of the anisotropic Heisenberg ferromagnet with both exchange and single-ion anisotropy the low-temperature renormalization of the spin-waves for the uniaxial ordering agrees with the Bloch-Dyson theory. For the spin-1 easy-plane ferromagnet, the critical parameters for the phase transition at zero temperature are determined and compared with other theories. The elementary excitation spectrum of the spin-1 isotropic quadrupolar system is calculated and compared with the random phase approximation and Callen-like decoupling schemes. Finally, the theory is applied to the study of the single-particle excitation spectrum of the Hubbard model.

Self-consistent many-body theory for the standard basis operator Green's functions

We propose a model for electrons existing in hybridized narrow and wide bands which occur in the transition metals, the mixed valence systems of rare earth metals and their compounds, and the doped semiconductors, etc. The model is derived from the standard basis operator (SBO) form of the extended Anderson model, originally proposed for the dilute magnetic alloys. The equation of motion method has been used to obtain the SBO's Green's functions and, thereby, the spectrum of the quasi-particle excitations. For translationally invariant systems, we found the possibility of the nonmetallic behavior and the metal-nonmetal transition for a nonintegral number of electrons per lattice site.

R. Kishore

Papers

Self-consistent many-body theory for the standard basis operator Green's functions

A model for electrons existing in hybridized narrow and wide bands