Strong-coupling approach for strongly correlated electron systems

Abstract

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'').

14 pages, revtex, feynmf, 5 EPS figures, two-column PRB style, published in PRB

References in corpus (3)

• Optimization of alloy-analogy-based approaches to the infinite-dimensional Hubbard model
• Pseudospin-Electron Model in Large Dimensions
• Structure of the Hilbert-space of the infinite-dimensional Hubbard model

Cited by in corpus (8)

• Electronic Structure Calculations with Dynamical Mean-Field Theory: A Spectral Density Functional Approach
• Dynamical mean-field theory of correlated hopping: A rigorous local approach
• Strong Coupling Theory for Interacting Lattice Models
• Extremely Correlated Quantum Liquids
• Quasiparticle states of the Hubbard model near the Fermi level
• Equation of Motion Series Expansion of Double Time Green's Functions
• Correlated hopping in infinite dimensions: Rigorous local approach
• Electron-hole asymmetry in electron systems with orbital degeneracy and correlated hopping