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Physical review. B, Condensed matter

Superconductivity in correlated systems: Constraint quantization of slave bosons

Mariusz Krawiec, Karol Izydor Wysokiński

Published Apr 1, 1999• 5 citations
Publisher

Abstract

The quantization rules obtained by Le Guillou and Ragoucy in the slave particle theories of correlated systems have been applied to study the superconductivity in extended Hubbard and $t\ensuremath{-}J$ models. The quantization scheme has the virtue of treating the local constraint exactly. We compare our numerical results with those obtained in the mean-field approximation for usual slave boson technique. We also discuss the relation of the present approach with method of equation of motion for Hubbard operators. Where possible the obtained results are also compared with experimental data on high-temperature superconductors, as in these materials the essential physics is believed to depend on the presence of strong correlations.

DOI
10.1103/physrevb.59.9500

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The quantization rules obtained by Le Guillou and Ragoucy in the slave particle theories of correlated systems have been applied to study the superconductivity in extended Hubbard and t\ensuremath−Jt\ensuremath{-}Jt\ensuremath−J models. The quantization scheme has the virtue of treating the local constraint exactly. We compare our numerical results with those obtained in the mean-field approximation for usual slave boson technique. We also discuss the relation of the present approach with method of equation of motion for Hubbard operators. Where possible the obtained results are also compared with experimental data on high-temperature superconductors, as in these materials the essential physics is believed to depend on the presence of strong correlations.
The superfluid characteristics of the attractive Hubbard model are analyzed for any coupling |U| and arbitrary electron concentration (0n2) by means of the slave-boson mean-field method and also by the perturbative treatment of the strong-coupling limit. The slave boson method takes into account correlations of electrons and yields a reliable description of the crossover from BCS-type superconductivity to local pair (composite bosons) superconductivity with increasing |U|. The results for the ground state (the free energy, the gap in the excitation spectrum) and the electromagnetic characteristics (the critical magnetic field, the London penetration depth, the coherence length) are compared with those obtained by the Hartree-Fock approximation and by the self-consistent second-order perturbation theory in the weak-coupling limit as well as with those obtained using perturbational approaches in the strong-coupling limit. We show that the slave-boson method, in contrast to the Hartree-Fock approximation, gives credible results for all investigated quantities in the whole interaction range, interpolating smoothly between the BCS and local pair regimes. A comparison of theoretical predictions for our simple model with experimental data for various families of short-coherence-length superconductors suggests that the best agreement can be obtained for intermediate values of the local attraction. \textcopyright{} 1996 The American Physical Society.
We investigate the possibility of superconductivity in the large-UUU limit of the Hubbard model near half filling, using a slave-boson representation. The local constraint is treated in a novel way, incorporating short-range fluctuations in addition to the global constraint. We find slave-boson pairing and a superconducting extended sss-wave phase at hole concentrations $\ensuremath{\delta}$-above 4% and below 32%.
In this paper we generalize slave-boson mean-field theory for $t\ensuremath{-}J$ model to the time-dependent regime, and derive transport equations for $t\ensuremath{-}J$ model, both in the normal and superconducting states. By eliminating the boson and constraint fields exactly at zero temperature in the linear-response regime we obtain a set of transport equations for physical electrons which have the same form as Landau transport equations for normal Fermi liquid and Fermi-liquid superconductor, respectively, with all Landau parameters explicitly given. Our theory can be viewed as a refined version of U(1) Gauge theory where all lattice effects are retained and strong correlation effects are reflected as strong Fermi-liquid interactions in the transport equation. Some experimental consequences are discussed.
We study superconductivity in the extended Hubbard model with a strong on-site repulsion U and weak attractive density-density interaction Vij{\mathit{V}}_{\mathit{ij}}Vij​. The electron correlation effects, beyond the weak-coupling regime of U, are included approximately by employing Hubbard decoupling approximations. The formulas for superconducting transition temperature Tc{\mathit{T}}_{\mathit{c}}Tc​ of the present approach are compared to those obtained with the strong-coupling expansion and slave-boson techniques. The methods share some common features. We discuss behavior of Tc{\mathit{T}}_{\mathit{c}}Tc​ for superconducting phases with s- and d-wave symmetry of the superconducting order parameter. In contrast to the mean-field treatment of U, we find that the strong on-site repulsion does not destroy superconductivity induced by ${\mathit{V}}_{\mathit{ij}}$0 even when U\ensuremath{\gg}|${\mathit{V}}_{\mathit{ij}}$|. \textcopyright{} 1996 The American Physical Society.
We start from the Barnes-Coleman slave-particle description, where the Hubbard operators X are decomposed into a product of fermionic (fα) and bosonic (b) operators. The quantum mechanical constraint b † b+ ∑ α f † αfα = 1 is treated within the framework of Dirac’s method for the quantization of classical constrained systems. This leads to modified algebraic properties of the fundamental operators: bb † b = b, fαf † βfγ = δαβfγ and fαb † = 0. Thereby the algebra of the X-operators is preserved exactly on the operator level. Matrix representations of the above algebra are constructed and a resolvent-like perturbation theory for the single-impurity Anderson model is developed.
Slave boson mean-field studies of the ground state of the Hubbard model with correlated hopping were performed. The approach qualitatively recovers the exact results for the case when the hopping integral ttt equals the correlated hopping integral X.X.X. The phase diagram for the strongly correlated state with only singly occupied sites, the weakly correlated state, where single and double occupation is allowed, and for the superconducting state, was determined for any value of XXX and any electron concentration n.n.n. At the half-filled band (n=1)(n=1)(n=1) a direct transition from the superconductor to the Mott insulator was found. In the region of strong correlations the superconducting solution is stable for nnn close to 1, in contrast to the case of weak correlations, in which superconductivity occurs at $n\ensuremath{\approx}0$ and $n\ensuremath{\approx}2.$ We have also found that strong correlations change the characteristics of the superconducting phase, e.g., the gap in the excitation spectrum exhibits a nonexponential dependence on the on-site Coulomb integral UUU close to the phase-transition point.