By Andryan A. A.

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There are 8 operators of Fermi type X 0σ , X σ0 , X σ2 , X 2σ , 4 nondiagonal Bose type operators X +− , X −+ , X 20 , X 02 , and 4 diagonal Bose type operators. X 00 , X ++ , X −− , X 22 . June 28, 2004 11:0 WSPC/Book Trim Size for 9in x 6in chap01 Hubbard Model as a Simplest Model of Strong Electron Correlations 19 For the Hubbard model the X-operators can be expressed via the Fermi operators af σ : Xf0,0 = (1 − nf ↑ )(1 − nf ↓ ), Xfσ,σ = nf,σ (1 − nf,−σ ), Xfσ,0 = a+ f,σ (1 − nf,−σ ), Xfσ,−σ = a+ f,σ af,−σ , Xf2,2 = nf ↑ nf ↓ , Xf2,σ = 2σa+ f,−σ nf,σ , + Xf2,0 = 2σa+ f,−σ af,σ .

For the s–d model with U = ∞ and J = +∞ the same procedure as that used by Nagaoka (1966) results in the exact ferromagnetic ground state in the following situations: (1) number of electrons Ne = N n+1 (one extra electron on the background of dn -ions), (2) Ne = N (n + 1) ± 1 (one extra electron or hole on the background of high spin S + 1/2), and (3) Ne = N (n + 2) − 1 (one hole on the background of s2 dn -conﬁgurations with spin S). 4 The Periodic Anderson Model In this model the localized d (f ) electron may ﬂuctuate between the two multielectron conﬁgurations of dn with spin Sn and dn+1 with spin Sn+1 .

Chap02 June 28, 2004 11:2 WSPC/Book Trim Size for 9in x 6in Chapter 3 General Approach to the Quasiparticle Description of Strongly Correlated Systems The idea that an electron is a quasiparticle of the Landau Fermi liquid theory cannot be applied straightforwardly in the SEC systems because the SEC changes the ground state and may result in the metal–insulator transition with the Fermi surface disappearing at all. ) as the excitations for the multielectron systems. In this chapter the deﬁnition of the Fermi and Bose quasiparticles will be given and the scheme to calculate their dispersion law which we call the generalized tight-binding (GTB) method is considered.