Slave-boson

Keywords High-Tc cuprates, effective band-structure, slave boson method, La2 Sr Cu04... 

In this paper, we show that the observed band-properties can be described within the CT limit of the Emery model, taking into account, beyond the perturbation level, the direct oxygen-oxygen overlap t, treated by the infinite U paramagnetic slave boson method. 

It is also important to note that the slave boson method itself possess two different types of symmetry with respect to doping. From the doping dependence of the effective copper-oxygen overlap t for Ap(i/t0 large enough, symmetry with respect to zero doping emerges [8], since... 

An alternative approach is the Slave Boson approximation [21] where the Fermionic operators are defined as the product of Boson and spin operators. There is a constraint with the number of Fermions, n /, and number of Bosons, n n f - - m, = 1. The spin part is treated with a RVB spin model and the charge as a Bose-Einstein condensation problem. These leads to a fractionalization of charges (holons) and spin (spinons), where uncondensed holons exist above the SC domain. The temperature crossover of the spinon pairing and the holon condensation, as a function of doping, is identified as peak in the SC domain. 

The computational technique used to treat the generalized Anderson impurity model in the slave boson representation will be described in some detail. For an extensive discussion see Coleman (1984). In Appendix A we represented the CEF states of stable 4f" shells (i.e., with integer occupation n) by pseudofermions. In the present case of unstable shells with possible 4f and 4f configurations we need an additional slave boson field for the 4f° state. The interesting physical quantities, static as well as dynamic, can be calculated in terms of the fully renormalized fermion and slave boson Matsubara Green s functions... 

We present a short derivation of these integral equations using Colemans slave boson (sb) approach. In this approach an auxiliary boson is introduced as a bookkeeping device for the number of f-electrons (Barnes 1976), and the Hamiltonian is written as... 

In the calculation of the f Green s function as defined in (22) one has to make sure that the intermediate N — 1)- and (N + l)-electron states are in the Q = 1 subspace as well. This can be achieved by creating (annihilating) a boson when the f-electron is removed (added). The true f-propagator in the slave boson approach is therefore given by G defined as... 

Apart from the necessity to project onto the physical subspace Fj, the form of the slave boson Hamiltonian H b has the advantage that usual many-body techniques, like the generalization of Wick s theorem to finite temperatures, can be used to produce a systematic perturbation expansion in the mixing term. Coleman performs such an expansion neglecting the restriction on Q and carries out the projection onto the 2 = 1 subspace in the end of the calculation. For that purpose he extended Abrikosov s scheme (Abrikosov 1965, Barnes 1976) of weighting the 2 > 1 states by... 

Below we briefly review a few of the developments after this chapter had been submitted (February, 1986). There has been a substantial amount of work on the extension of the impurity model to a lattice model. Rice and Ueda (1985) and Fazekas and Brandow (1987) used a generalized Gutzwiller ansatz for the spin-degenarate Anderson lattice. Saso and Seino (1986) and Blankenbecler et al. (1987) used the Monte Carlo technique for studying a finite one-dimensional chain. Millis and Lee (1987) used the slave boson formalism for the large degeneracy Anderson lattice. A renormalization group calculation has also been performed for the two-impurity model by Jones and Varma (1987). 

Fig. 35. Predictions of a slave-boson treatment of a Kondo insulator for the specific heat Cp (solid line) and temperature derivative of the f-occupation number dUf/dT (solid circles). As opposed to the Anderson impurity model, where dnf/dT peaks at a temperature which is 2-3 times larger than the temperature where Cp is maximum, for this Anderson Lattice calculation both quantities peak at roughly the same temperature. From Riseborough (1992).

Thalmeier (1988) has calculated the adiabatic bulk modulus of the Anderson Lattice by including a strain dependence of Lkf Lkf —> Kkf + (dVy Vyds)s. Using a slave-boson method for e = 0 and second order perturbation theory with respect to dVkf(V)/ds, he finds... 

Slave-Boson Approach to Strongly Correlated Electron Systems... 

Hamiltonian of the t-J model (Eq. 3) in terms of the slave-boson and pseudofermion operators has to be replaced by... 

Figure 7.7 Doping dependence of the Hall resistivity for hole-doped (left panel) and electron-doped (right panel) systems. The slave-boson results for J t = 0.4 and different ratios t lt = 0 (solid), -0.16 (dashed), -0.4 (chain dotted) and t lt = 0.16 (dotted) are compared with experiments on LSCO ( ) [53] (at 80 K), YBCO (A) [54] (at 100 K) and NCCO (O) [55, 56] (at 80 K), respectively. The inset shows the temperature dependence of Rg for t lt = 0 at 5 = 0.1 (short dashed) and d = 0.15 (dotted).

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