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Journal of Physics Condensed Matter

Spiral magnetic states in the large-U Hubbard model: a slave boson approach

Raymond Frésard, P. Wölfle

Published Mar 30, 1992• 71 citations
Publisher

Abstract

The authors determine the ground state phase diagram of the Hubbard model on the square lattice allowing for homogeneous spiral, antiferromagnetic, ferromagnetic and paramagnetic phases. This is obtained from a saddle-point approximation of a spin-rotation-invariant form of the slave boson representation introduced by Kotliar and Ruckenstein. They obtain very good agreement in energy with exact diagonalization calculations and, concerning the magnetic structure, qualitative agreement with experimental data.

DOI
10.1088/0953-8984/4/13/022

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The authors determine the ground state phase diagram of the Hubbard model on the square lattice allowing for homogeneous spiral, antiferromagnetic, ferromagnetic and paramagnetic phases. This is obtained from a saddle-point approximation of a spin-rotation-invariant form of the slave boson representation introduced by Kotliar and Ruckenstein. They obtain very good agreement in energy with exact diagonalization calculations and, concerning the magnetic structure, qualitative agreement with experimental data.
The authors determine the ground-state phase diagram of the Hubbard model on the square lattice allowing for homogeneous spiral, antiferromagnetic, ferromagnetic and paramagnetic phases in the overall parameter range. This is obtained from a saddle-point approximation of a spin-rotation-invariant form of the slave-boson representation introduced by Kotliar and Ruckenstein (1986). In addition they determine analytically the transition point for infinite repulsive interaction strength between the Nagaoka state and the paramagnetic state on any bipartite lattice.
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 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 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 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.