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Physical review. B, Condensed matter

Dynamical charge response function of the Hubbard model in the slave-boson approach

T. Li

Published Oct 15, 1992• 6 citations
Publisher

Abstract

A concise general expression for the dynamical charge susceptibility of the Hubbard model is presented. The results are obtained from the spin-rotation-invariant slave-boson theory, whose paramagnetic saddle point corresponds to Gutzwiller's variational approximation. The charge structure factor and charge susceptibility are calculated for a wide range of interactions and temperatures and are compared thoroughly with the available quantum Monte Carlo and variational Monte Carlo results for the one-dimensional Hubbard model. The comparison shows reasonable agreement. All the calculations are done in a totally self-consistent way, without adjustable parameters.

DOI
10.1103/physrevb.46.9301

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A concise general expression for the dynamical charge susceptibility of the Hubbard model is presented. The results are obtained from the spin-rotation-invariant slave-boson theory, whose paramagnetic saddle point corresponds to Gutzwiller's variational approximation. The charge structure factor and charge susceptibility are calculated for a wide range of interactions and temperatures and are compared thoroughly with the available quantum Monte Carlo and variational Monte Carlo results for the one-dimensional Hubbard model. The comparison shows reasonable agreement. All the calculations are done in a totally self-consistent way, without adjustable parameters.
The spin and charge structure factors are calculated for the Hubbard model on the square lattice near half filling using a spin-rotation invariant six-slave boson representation. The charge structure factor shows a broad maximum at the zone corner and is found to decrease monotonically with increasing interaction strength and electron density and increasing temperature. The spin structure factor develops with increasing interaction two incommensurate peaks at the zone boundary and along the zone diagonal. Comparison with results of quantum Monte Carlo and variational calculations is carried out and the agreement is found to be good. The limitations of a random-phase-approximation type approach are pointed out.
We present a slave-boson representation for the Hubbard model, introducing Bose fields for the empty, singly, and doubly occupied sites and show that the boson for the singly occupied site must transform as a tensor of rank two under spin rotations. This generalizes the formulation of Kotliar and Ruckenstein, which is not manifestly spin-rotation invariant. The paramagnetic saddle point of the corresponding functional integral is identical to Gutzwiller's solution. As an illustration of the method, we calculate the T3{T}^{3}T3lnT spin-fluctuation contribution to the specific heat and find it to be fully consistent with Fermi-liquid theory. We discuss further applications of this approach.
We present a comprehensive study of the two-dimensional one-band Hubbard model applying the spin-rotation-invariant slave-boson method. We utilize a spiral magnetic mean field and fluctuations around a paramagnetic mean field to determine the magnetic phase diagram and find the two approaches to be in good agreement. Apart from the commensurate phases characterized by ordering wave vectors $\mathbf{Q}=(\ensuremath{\pi},\ensuremath{\pi})$, $(0,\ensuremath{\pi})$, and (0,0) we find incommensurate phases where the ordering wave vectors Q=(Q,Q)\mathbf{Q}=(Q,Q)Q=(Q,Q) and $(Q,\ensuremath{\pi})$ vary continuously with filling, interaction strength, or temperature. The mean-field quantities magnetization and effective mass are found to change discontinuously at the phase boundaries separating the (Q,Q)(Q,Q)(Q,Q) and $(Q,\ensuremath{\pi})$ phases, indicating a first-order transition. The band structure and Fermi surface is shown in selected cases. The dynamic spin and charge susceptibilities as well as the structure factors are calculated and discussed, including the emergence of collective modes of the zero sound and Mott insulator type. The dynamical conductivity is calculated in dependence of doping, interaction strength, and temperature. Finally, a temperature-interaction strength phase diagram is established.
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.
We present a comprehensive study of the 2D one-band Hubbard model applying the spin rotation invariant slave-boson method. We utilize a spiral magnetic mean field and fluctuations around a paramagnetic mean field to determine the magnetic phase diagram and find the two approaches to be in good agreement. Apart from the commensurate phases characterized by ordering wave vectors Q=(π,π),(0,π), and (0,0) we find incommensurate phases where the ordering wave vectors Q=(Q,Q), and (Q,π) vary continuously with filling, interaction strength or temperature. The mean field quantities magnetization and effective mass are found to change discontinuously at the phase boundaries separating the (Q,Q) and (Q,π) phases, indicating a first order transition. The band structure and Fermi surface is shown in selected cases. The dynamic spin and charge susceptibilities as well as the structure factors are calculated and discussed, including the emergence of collective modes of the zero sound and Mott insulator type. The dynamical conductivity is calculated in dependence of doping, interaction strength and temperature. Finally, a temperature-interaction strength phase diagram is established.
We consider slave boson formulations of the Hubbard model, the t–J model and the Anderson model, in which spin and charge fermion degrees of freedom are represented by Bose fields. The approach has been applied to the Hubbard model generalizing the formulation of Kotliar and Ruckenstein. There the Gutzwiller solution is recovered as a saddle point. The method allows to find other types of mean field solutions in a systematic way. Dynamical correlation functions in mean field approximation as well as fluctuation contributions are also calculated.