Thermodynamics of Pseudospin-Electron Model in Mean Field Approximation

Abstract

The mean field type approach based on the self-consistent consideration of an effective field created by electron transfer is developed for a description of thermodynamics of the Hubbard type models with an infinitely large on-site repulsion. This procedure, formulated according to [1], is an extension of the recently proposed generalized random phase approximation(GRPA).Within this approach, the thermodynamic properties of the two-sublattice pseudospin-electron model (the Hubbard model with local anharmonicity) are studied. Such a model can be used for a description of dielectric properties of YBaCuO-type superconductors along c-axis; pseudospins represent anharmonic motions of apical oxygens O4. It is shown that there are either phase transitions in the model with jumps of the mean values of a pseudospin and of electron concentration (in the µ = const regime) or the phase separation (in the n = const regime). The phase transitions or phase separation are caused by pseudospin-pseudospin interaction as well as by electron transfer (the latter results in appearing of effective interaction between pseudospins). The possibility of the ferroelectric type ordering of pseudospins is investigated.

Green's Functions of Infinite-U Asymmetric Hubbard Model: Falicov-Kimball Limit

“…Let us note that in the case of the pseudospin-electron model (PEM) without tunnelling, the dynamics of pseudospins being analogous to the Falicov-Kimball model, the regime of µ B = const corresponds to the fixation of longitudinal asymmetry field h acting on pseudospins. The PEM thermodynamics has been a subject of investigations within DMFT [21] as well as in the framework of approximate methods (generalized random phase approximation (GRPA), [22][23][24]).…”

Phase Transitions in the Pseudospin-Electron Model

“…Two-sublattice PEM 35,36,37,38,76 appeared as a generalization of the usual PEM with the aim of more realistic description of the anharmonic subsystem of the apex oxygen ions in the YBaCaO type structures. In this case the pseudospin energy in the internal field is of the form h i (S z i1 − S z i2 ) that is the reflection of the mirror symmetry of the problem.…”

“…The case is considered, when the chemical potential is placed in the region of energy subbands (α = 1, 2) ε31 α (k) = ε41 α (k) = (−1) α g 2 + t k X44 α + X11 α 0 (92) separated by the gap equal to g. The Hubbard-I approximation in which the expressions (92) are given here, was improved in Ref. [38] by the meanfield corrections (being of the form of the loop-like inclusions) to the electron Green's functions. Thus, renormalization of spectrum due to the shift of subbands dependent on electron concentration was taken into account.…”

“…34 In the case of two-sublattice PEM the structural instabilities of the ferroelectric type as well as the bistability phenomena were revealed and analysed. 35,36,37,38 The study of the PEM thermodynamics was performed mainly within the generalized random phase approximation (GRPA). 39 A method of dynamical mean field theory (DMFT) was used in the case of simplified PEM, 29 when the analytic formulation of the theory is possible.…”