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physica status solidi (b)

On Antiferromagnetism, Charge Density Wave, and Superconductivity in the Extended Hubbard Model Studied by Means of the Slave‐Boson Method

Bogdan R. Bułka

Published Dec 1, 1993• 6 citations
Publisher

Abstract

Abstract The ground state of the extended Hubbard model is studied. The stability conditions for the antiferromagnetic, the charge density wave, and the superconducting state are analyzed in the same slave‐boson representation, which is spin‐ and charge‐rotationally invariant. It is found that at the concentration of electrons no = 1 the stable solutions are similar in form.

DOI
10.1002/pssb.2221800212

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Using the slave-boson method in its spin-and charge-rotational invariant representation we determine stability of the superconducting state in the Hubbard model with correlated hopping.In general the term with correlated hopping violates electron-hole symmetry, however, in the special case when the correlated hopping integral X is equal to the uncorrelated hopping inte- gral t the electron-hole symmetry remains.We investigate this case and show that correlations induced by onsite Coulomb interactions U yield to the nor- mal state with exactly single occupied sites (corresponding to |U = oo)).The phase diagram of the superconducting state is determined for the different electron concentration n.At the half-filled band (n = 1) a direct transition from the Mott insulator to the superconducting state occurs.
We study the two-dimensional one-band Hubbard model on the square lattice through the spin rotation invariant Kotliar-Ruckenstein slave-boson method, with an emphasis on the electron-doped regime. The phase diagram determined within mean field approximation reveals three different magnetically ordered phases separated by first-order transitions, and a wide instability region as indicated by a negative compressibility. We show that this conundrum of the unstable mean field domain is resolved by spatially mixed phases of neighboring stable states. We also find charge density wave type instabilities in the antiferromagnetically ordered (AFM) state at wave vectors commensurate with the doping. The corresponding charge and spin density response functions are calculated from a Gaussian fluctuations formalism about a magnetic saddle point, for which we provide a detailed derivation. Further, we present density and spin excitation spectra in the AFM phase, allowing for a quantitative calculation of the spin wave parameters, the gap in the longitudinal spin excitation spectrum, and the density excitations in the upper Hubbard band.
We use the extended Hubbard model to investigate the properties of the charge- and spin-density-wave phases in the presence of a nearest-neighbors repulsion term in the framework of the slave-boson technique. We show that, contrary to Hartree–Fock results, an instablity may occur for sufficiently high values of the Hubbard repulsion, both in the spin- and charge-density-wave phase, which makes the system discontinuously jump to a phase with a smaller or zero wave amplitude. The limits of applicability of our approach are discussed and our results are compared with previous numerical analysis. The phase diagram of the model at half-filling is determined.
We use the Kotliar-Ruckenstein slave boson formalism to study the phase diagram of the doped antiferromagnetic Mott insulator at zero and finite temperatures. We obtain the commensurate magnetic phase diagram as a function of doping and temperature. At higher doping and temperatures we find a paramagnetic metallic phase. Reducing doping and temperature, we find antiferromagnetic phases with both metallic and insulating solutions. We calculate the electronic density of states in various regions of the phase diagram. We use our results for the electronic compressibility and magnetic susceptibility to analyze the stability of the various phases obtained within this mean field formalism. We find various parameter regimes where the method fails to provide physical solutions. We argue that those regions correspond to more exotic phases that cannot be described within the current mean field theory.
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.
Magnetic properties of Hubbard model have been studied extensively. A theoretical description of these states, however, is not straight forward within conventional mean-field approach due to the electron correlation effects. Here we provide a slave spin theory of the magnetic states in the single band Hubbard model. By introducing an additional decomposition of the on-site Coulomb interaction in the magnetic channel in both the slave spin and the fermionic spinon sectors, we show a magnetic solution with renormalized quasiparticle spectral weight can be stabilized at both half-filling and finite doping. By comparing the energies of antiferromagnetic and ferromagnetic states, we provide a ground-state phase diagram for generic electron filling. We further discuss possible generalization of the slave-spin method.