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arXiv:cond-mat/9807019 · Condensed Matter Physics

SYMMETRIES IN THE PHYSICS OF STRONGLY CORRELATED ELECTRONIC SYSTEMS

Mancini, Avella

Published Jan 1, 1998• 6 citations
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Abstract

Strongly correlated electron systems require the development of new theoretical schemes in order to describe their unusual and unexpected properties.The usual perturbation schemes are inadequate and new concepts must be introduced.In our scheme of calculations, the Composite Operator Method is possible to recover through a self-consistent calculation, a series of fundamental symmetries by choosing a suitable Hilbert space.

DOI
10.5488/cmp.1.1.11

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Strongly correlated electron systems require the development of new theoretical schemes in order to describe their unusual and unexpected properties.The usual perturbation schemes are inadequate and new concepts must be introduced.In our scheme of calculations, the Composite Operator Method is possible to recover through a self-consistent calculation, a series of fundamental symmetries by choosing a suitable Hilbert space.
In recent years the numerical renormalization group (NRG) method has been extended to the calculation of dynamic response functions and transport properties of magnetic impurity models. The approach can now be applied more widely to lattice models of strongly correlated electron systems by the use of dynamical mean field theory (DMFT), in which the lattice problem is transformed into one for an effective impurity with an additional self-consistency constraint. We review these developments and assess the potential for further applications of this approach. We also discuss an alternative approach to renormalization, renormalized perturbation theory, in which the leading asymptotically exact results for the low temperature regime for a number of magnetic impurity models can be obtained within finite order perturbation theory.
We study the 1/N expansion of a generic, strongly correlated electron model ( SU (N) symmetric Hubbard model with U=∞ and N degrees of freedom per lattice site) in terms of X operators. The leading order of the expansion describes a usual Fermi liquid with renormalized, stable particles. The next-to-leading order violates Luttinger's theorem if a finite convergence radius for the 1/N expansion for a fixed and non-vanishing doping away from half-filling is assumed. We find that the volume enclosed by the Fermi surface, is at large, but finite N's and small dopings larger than at N=∞. As a by-product an explicit expression for the electronic self-energy in O(1/N) is given which cannot be obtained by factorization or mode-coupling assumptions but contains rather sophisticated vertex corrections.