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Journal of Physics Conference Series

The intersite interactions in the problem of energy structure of the strongly correlated electron systems

Valerii Vladimirovich Val'kov, M. M. Korovushkin

Published Jan 1, 2010• 0 citations
Publisher

Abstract

On the basis of the extended set of the irreducible operators orthogonal on Mori an effect of the intersite interactions on the formation of energy structure of the t − V –model has been studied. Qualitative new result consists in the appearance of an additional fluctuation band in the structure of energy spectrum. The formation of the fluctuation band is connected with the deviation of the occupation numbers from the nominal value. The spectral intensity of the fluctuation band depends on the carrier concentration and rises when the root-mean-square fluctuations of the occupation numbers are increased. Consequently at increase doping level there is a redistribution of the spectral weight between ordinary band and fluctuation band in favour of the last. This redistribution underlies a modification of integrated density of states.

DOI
10.1088/1742-6596/200/1/012094

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Physical review. B, Condensed matter•Dec 15, 1994•158 citations
On the basis of the extended set of the irreducible operators orthogonal on Mori an effect of the intersite interactions on the formation of energy structure of the t − V –model has been studied. Qualitative new result consists in the appearance of an additional fluctuation band in the structure of energy spectrum. The formation of the fluctuation band is connected with the deviation of the occupation numbers from the nominal value. The spectral intensity of the fluctuation band depends on the carrier concentration and rises when the root-mean-square fluctuations of the occupation numbers are increased. Consequently at increase doping level there is a redistribution of the spectral weight between ordinary band and fluctuation band in favour of the last. This redistribution underlies a modification of integrated density of states.
The diagram technique for Hubbard operators is used to investigate the influence of intersite Coulomb interactions on the energy structure and Cooper instability of strongly correlated fermions. Allowance for intersite correlations in doped Mott-Hubbard insulators is shown to lead to a splitting of the lower subband of Hubbard fermions and to the formation of a band of fluctuation states as soon as the intersite interaction energy becomes comparable to or exceeds the mean kinetic energy. The spectral intensity of the splitoff band is proportional to the root-mean-square fluctuation of the occupation numbers and increases with doping level. The predicted effect changes significantly the structure of the density of electronic states. This leads to a renormalization of the pole of the scattering amplitude in the Cooper channel and manifests itself as a nonuniform (in electron concentration) modification of the dependence of the critical superconducting transition temperature.
The effect of the strong intersite Coulomb correlations on the formation of the electron structure of the t-V-model has been studied. A qualitatively new result has been obtained which consists in the occurrence of a split-off band of the Fermi states. The spectral intensity of this band increases with the enhancement of a doping level and is determined by the mean-square fluctuation of the occupation numbers. This leads to the qualitative change in the structure of the electron density of states.
Abstract The diagrammatic strong‐coupling perturbation theory (SCPT) for correlated electron systems is developed for intersite Coulomb interaction and for a nonorthogonal basis set. The construction is based on iterations of exact closed equations for many‐electron Green functions (GFs) for Hubbard operators in terms of functional derivatives with respect to external sources. The graphs, which do not contain the contributions from the fluctuations of the local population numbers of the ion states, play a special role: a one‐to‐one correspondence is found between the subset of such graphs for the many‐electron GFs and the complete set of Feynman graphs of weak‐coupling perturbation theory (WCPT) for single‐electron GFs. This fact is used for formulation of the approximation of renormalized Fermions (ARF) in which the many‐electron quasi‐particles behave analogously to normal Fermions. Then, by analyzing: (a) Sham's equation, which connects the self‐energy and the exchange–correlation potential in density functional theory (DFT); and (b) the Galitskii and Migdal expressions for the total energy, written within WCPT and within ARF SCPT, a way we suggest a method to improve the description of the systems with correlated electrons within the local density approximation (LDA) to DFT. The formulation, in terms of renormalized Fermions LDA (RF LDA), is obtained by introducing the spectral weights of the many‐electron GFs into the definitions of the charge density, the overlap matrices, effective mixing and hopping matrix elements, into existing electronic structure codes, whereas the weights themselves have to be found from an additional set of equations. Compared with LDA+U and self‐interaction correction (SIC) methods, RF LDA has the advantage of taking into account the transfer of spectral weights, and, when formulated in terms of GFs, also allows for consideration of excitations and nonzero temperature. Going beyond the ARF SCPT, as well as RF LDA, and taking into account the fluctuations of ion population numbers would require writing completely new codes for ab initio calculations. The application of RF LDA for ab initio band structure calculations for rare earth metals is presented in part II of this study (this issue). © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005
The spectral weight functions and the optical conductivity of a highly correlated electronic system described by a simple Hubbard model are studied. The calculations are carried out for a small system, a cubic cluster of eight sites, by means of exact diagonalization using symmetrized basis functions. The spectral weight functions of a single hole (or electron) placed in an otherwise half-filled band are obtained. The density of states at different interaction strengths, ranging from weak to strong couplings, is studied. We observe the spreading of the spectral weight associated with some single-particle eigenstates over a large range of energies, and the appearance of satellite structure at higher excitation energies. The nature of band narrowing is also discussed. The frequency dependent (optical) conductivity is studied for the cases of a half-filled band, and for one hole and two hole dopings away from half filling. The interaction strength is varied between the weak- and strong-coupling limits. The formation of a Hubbard gap is observed. Results are related to aspects of the metal-insulator transition in bulk systems.
Using strong-coupling perturbation theory for the Hubbard model, explicit expressions are obtained for the integrated weights, energy positions, and widths of the upper and lower Hubbard bands separately, both for the optical and photoemission spectrum. In one dimension all expressions can be explicitly evaluated using the large-U Bethe-ansatz wave function. The k\ensuremath{\rightarrow}-dependent moments for the one-particle spectrum are compared with the closely related two-pole ansatz. The strong momentum dependence of the spectra demonstrates the importance of the k\ensuremath{\rightarrow}-dependent correlation functions in the spectral moments, which are often neglected. In order to estimate corrections due to the neglect of higher-order terms (in t/U), all results are compared with numerical-diagonalization data for intermediate-U values. The sum-rule results show a rapid spectral-weight transfer from the high- to the low-energy regime upon doping, similar to what is observed experimentally in one-particle and optical spectra of Cu (high-Tc{\mathit{T}}_{\mathit{c}}Tc​) and Ni compounds. Such fast weight redistributions as a function of the carrier density are a natural consequence of the strong correlations in these materials. The redistribution of intensity in the optical conductivity is connected with the dilution of the spin system by the added holes. For the one-particle spectrum the decrease of weight in the upper Hubbard band away from half filling can be understood by state counting at U=\ensuremath{\infty}, and the effect is strongly enhanced for small doping by both the first- and second-order terms in t/U. Altogether, the one-particle and optical spectra show the importance of the three-site hopping term. Therefore the t-J model does not represent well the spectral properties of the Hubbard model at large U. The local spin order is essential and determines both the k\ensuremath{\rightarrow} dependence of the one-particle spectrum and the intensities in the optical spectrum.