Nonresonant Raman and inelastic X-ray scattering in the charge-density-wave phase of the spinless Falicov-Kimball model

Nonresonant inelastic light and X-ray scattering is investigated for the spinless Falicov-Kimball model on an infinite-dimensional hypercubic lattice with a charge-density-wave phase at half filling. The many-body density of states (DOS) is found for different values of the Coulomb repulsion $U$, ranging from a dirty metal to a Mott insulator. At zero temperature, the charge gap is exactly equal to $U$; increasing the temperature rapidly fills the gap with subgap states. The nonresonant response function for Raman and inelastic X-ray scattering shows peaks connected with transitions over the gap and transitions that involve subgap states. In the case of X-ray scattering (when both energy and momentum are transferred), the response function illustrates features of dynamical screening (vertex corrections) in the different (nonresonant) symmetry channels ($A_{\rm 1g}$ and $B_{\rm 1g}$). We also derive and verify the first moment sum rules for the (nonresonant) Raman and inelastic X-ray response functions.Comment: 19 pages, 17 figure

Hydrogen transport in superionic system Rb3H(SeO4)2: a revised cooperative migration mechanism

We performed density functional studies of electronic properties and mechanisms of hydrogen transport in Rb3H(SeO4)2 crystal which represents technologically promising class M3H(XO4)2 of proton conductors (M=Rb,Cs, NH4; X=S,Se). The electronic structure calculations show a decisive role of lattice dynamics in the process of proton migration. In the obtained revised mechanism of proton transport, the strong displacements of the vertex oxygens play a key role in the establishing the continuous hydrogen transport and in the achieving low activation energies of proton conduction which is in contrast to the standard two-stage Grotthuss mechanism of proton transport. Consequently, any realistic model description of proton transport should inevitably involve the interactions with the sublattice of the XO4 groups.Comment: 11 pages, 11 figures, to appear in Physical Review

Phase transitions and quantum effects in anharmonic crystals

The most important recent results in the theory of phase transitions and quantum effects in quantum anharmonic crystals are presented and discussed. In particular, necessary and sufficient conditions for a phase transition to occur at some temperature are given in the form of simple inequalities involving the interaction strength and the parameters describing a single oscillator. The main characteristic feature of the theory is that both mentioned phenomena are described in one and the same setting, in which thermodynamic phases of the model appear as probability measures on path spaces. Then the possibility of a phase transition to occur is related to the existence of multiple phases at the same values of the relevant parameters. Other definitions of phase transitions, based on the non-differentiability of the free energy density and on the appearance of ordering, are also discussed

Phase Separation and Charge-Ordered Phases of the d = 3 Falicov-Kimball Model at T>0: Temperature-Density-Chemical Potential Global Phase Diagram from Renormalization-Group Theory

The global phase diagram of the spinless Falicov-Kimball model in d = 3 spatial dimensions is obtained by renormalization-group theory. This global phase diagram exhibits five distinct phases. Four of these phases are charge-ordered (CO) phases, in which the system forms two sublattices with different electron densities. The CO phases occur at and near half filling of the conduction electrons for the entire range of localized electron densities. The phase boundaries are second order, except for the intermediate and large interaction regimes, where a first-order phase boundary occurs in the central region of the phase diagram, resulting in phase coexistence at and near half filling of both localized and conduction electrons. These two-phase or three-phase coexistence regions are between different charge-ordered phases, between charge-ordered and disordered phases, and between dense and dilute disordered phases. The second-order phase boundaries terminate on the first-order phase transitions via critical endpoints and double critical endpoints. The first-order phase boundary is delimited by critical points. The cross-sections of the global phase diagram with respect to the chemical potentials and densities of the localized and conduction electrons, at all representative interactions strengths, hopping strengths, and temperatures, are calculated and exhibit ten distinct topologies.Comment: Calculated density phase diagrams. Added discussions and references. 14 pages, 9 figures, 4 table

Strong-coupling approach for strongly correlated electron systems

A perturbation theory scheme in terms of electron hopping, which is based on the Wick theorem for Hubbard operators, is developed. Diagrammatic series contain single-site vertices connected by hopping lines and it is shown that for each vertex the problem splits into the subspaces with ``vacuum states'' determined by the diagonal Hubbard operators and only excitations around these vacuum states are allowed. The rules to construct diagrams are proposed. In the limit of infinite spatial dimensions the total auxiliary single-site problem exactly splits into subspaces that allows to build an analytical thermodynamically consistent approach for a Hubbard model. Some analytical results are given for the simple approximations when the two-pole (alloy-analogy solution) and four-pole (Hartree-Fock approximation) structure for Green's function is obtained. Two poles describe contribution from the Fermi-liquid component, which is dominant for small electron and hole concentrations (``overdoped case'' of high-$T_c$'s), whereas other two describe contribution from the non-Fermi liquid and are dominant close to half-filling (``underdoped case'').Comment: 14 pages, revtex, feynmf, 5 EPS figures, two-column PRB style, published in PR