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International Journal of Modern Physics B

ON THE THERMODYNAMICAL PROPERTIES IN THE SLAVE BOSON MEAN FIELD THEORY OF HUBBARD MODEL

M. ISODA

Published Jan 1, 1993• 0 citations
Publisher

Abstract

The effect of spin polarization in the slave boson mean field theory in the strongly correlated Heavy electron systems is discussed concerning the thermodynamical properties of the Hubbard model. The free energy is evaluated by taking into account the effective reduction of the quantum states due to the exclusion of double occupation in a site through the introduction of the spin-dependent slave boson. The magnetic susceptibility, calculated as a function of temperature, shows the Fermi liquid property at low temperature and the local moment behaviour with the proper Curie constant at high temperature. The present results, including the temperature dependence of the specific heat, are compared with the previous results without the reduction of quantum states.

DOI
10.1142/s0217979293001256

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The effect of spin polarization in the slave boson mean field theory in the strongly correlated Heavy electron systems is discussed concerning the thermodynamical properties of the Hubbard model. The free energy is evaluated by taking into account the effective reduction of the quantum states due to the exclusion of double occupation in a site through the introduction of the spin-dependent slave boson. The magnetic susceptibility, calculated as a function of temperature, shows the Fermi liquid property at low temperature and the local moment behaviour with the proper Curie constant at high temperature. The present results, including the temperature dependence of the specific heat, are compared with the previous results without the reduction of quantum states.
We use the Kotliar-Ruckenstein slave-boson formalism to study the temperature dependence of paramagnetic phases of the one-band Hubbard model for a variety of band structures. We calculate the Fermi liquid quasiparticle spectral weight ZZZ and identify the temperature at which it decreases significantly to a crossover to a bad metal region. Near the Mott metal-insulator transition, this coherence temperature Tcoh{T}_{\mathrm{coh}}Tcoh​ is much lower than the Fermi temperature of the uncorrelated Fermi gas, as is observed in a broad range of strongly correlated electron materials. After a proper rescaling of temperature and interaction, we find a universal behavior that is independent of the band structure of the system. We obtain the temperature-interaction phase diagram as function of doping, and we compare the temperature dependence of the double occupancy, entropy, and charge compressibility with previous results obtained with dynamical mean-field theory. We analyze the stability of the method by calculating the charge compressibility.
We review the slave-boson representations of the Hubbard model. When both spin and charge fermion degrees of freedom are represented by Bose fields, the approach is equivalent at the "self-consistent" saddle point level to the Gutzwiller approximation (GA). We show how the determination of the Lagrange multipliers, introduced to enforce the constraints, involves a Mott-Hubbard gap near half-filling for U > U c (localization edge). The quantum fluctuations are then considered within a renormalized basis of boson fields (restoring the spin-rotation invariance), which brings out two distinct channels, symmetric and antisymmetric. It is remarkable that both spin and charge fluctuations are obtained at the same level of the gaussian fluctuations, as oppossed to the standard 1/N expansion. This provides the microscopic basis for a Fermi liquid theory. Both dynamic effects and extension to finite temperature which were beyond the scope of the variational procedure can now be described by this approach. The physical implications of the model (dynamic correlation functions, T3Ln T term of the specific heat, superfluid instability) are finally considered, all of which reflect the Fermi liquid nature of the system.
High-temperature expansions for the specific heat and susceptibility of the strongly correlated Hubbard model are compared with corresponding quantities for spinless free fermions and free spins. It is found numerically that, when the temperature is high, the ratio of the specific heat of the strongly correlated Hubbard model to that of spinless free fermions approaches a particle-density-dependent constant. For fixed temperature, the susceptibility of the Hubbard model is less (greater) than that of free spins when the particle density is below (above) a certain threshold density of approximately 0.7. The ratio of the susceptibilities for the two systems, however, appears to be finite for any value of the particle density. Given that the free spin system does not have a ferromagnetic state at any finite temperature, it is concluded that the strongly correlated Hubbard model does not have a finite phase transition temperature. This conclusion is consistent with recent high-temperature expansion studies.
In order to contribute to understand well the thermodynamic properties of strongly correlated electron systems, we study numerically, in the grand canonical ensemble, the temperature dependence of the internal energy, specific heat, entropy, magnetization, and magnetic susceptibility of the one-dimensional Hubbard model without transference of moment in the interactions. The results have been obtained for a wide range of values of the on-site Coulombian repulsion U and of the external magnetic field h. Differences between this model and the original Hubbard model have been observed in relation to the number of peaks of the specific heat and to the behavior of the susceptibility in temperatures tending to zero. These differences evidence that the two models possess different magnetic structures of correlation.
We examine the two existing slave-boson methods for the finite-U Hubbard model by Kotliar and Ruckenstein (KR) and by Newns et al. and Zou and Anderson (NZA) in the light of the Fermi-liquid quasiparticle picture. It is shown that to treat doubly occupied states the KR slave-boson scheme is more consistent with this picture and that the well-known erroneous gauge-symmetry breaking encountered in the mean-field treatment of the NZA double-occupancy boson is due to the presence of the hidden double-fermion operators. Then, the effective intersite antiferromagnetic interaction between quasiparticles is derived in the KR slave-boson approach by taking into account empty and double-occupancy slave-boson fluctuations to O(1/N2{\mathit{N}}^{2}N2) in the 1/N expansion of the functional-integral formalism. The obtained effective exchange coupling constant Jeff{\mathit{J}}_{\mathrm{eff}}Jeff​(\ensuremath{\delta})=J(2p02{\mathit{p}}_{0}^{2}p02​-\ensuremath{\delta}/2) with J\ensuremath{\equiv}tij2{\mathit{t}}_{\mathit{i}\mathit{j}}^{2}tij2​/U is strongly dependent upon doping \ensuremath{\delta} and is scaled with the reduced Coulomb repulsion u\ensuremath{\equiv}U/Uc{\mathit{U}}_{\mathit{c}}Uc​ in the two-dimensional (2D) and 3D Hubbard models, where Uc{\mathit{U}}_{\mathit{c}}Uc​ is the critical value for the metal-to-insulator transition. The roles of this intersite correlation and the spin-dependent band-renormalization correlation included in the mean-field theory for the paramagnetic-to-antiferromagnetic instability are compared in the two Hubbard models. The intersite contribution is more significant in the 2D case than in the 3D case, but is generally small compared with the band effect except for small dopings \ensuremath{\delta} and smaller U values. The maximum doping ${\mathrm{\ensuremath{\delta}}}_{\mathrm{cr}}$ for the paramagnetic-to-ferromagnetic instability in the strong-coupling limit (U\ensuremath{\rightarrow}\ensuremath{\infty}) of the 2D and 3D Hubbard models is found to be ${\mathrm{\ensuremath{\delta}}}_{\mathrm{cr}}$\ensuremath{\sim}0.28 and ${\mathrm{\ensuremath{\delta}}}_{\mathrm{cr}}$\ensuremath{\sim}0.38, respectively.
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.