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Physical review. B, Condensed matter

Spin disorder in the two-dimensional Hubbard model: A mean-field theory

Giovanni Vignale

Published Mar 1, 1991• 1 citation
Publisher

Abstract

A scheme of symmetry breaking is proposed for the two-dimensional Hubbard model at less than half filling. The self-induced mean field is a random spin-dependent potential. The energy of the spin-disordered state is shown to be lower than that of commensurate or incommensurate antiferromagnetic states. Long-wavelength charge and spin fluctuations obey the diffusion equation, leading to deviations from Fermi-liquid behavior. At wave vector q=(\ensuremath{\pi},\ensuremath{\pi}) the transverse spin-excitation spectrum has a gap.

DOI
10.1103/physrevb.43.6216

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A scheme of symmetry breaking is proposed for the two-dimensional Hubbard model at less than half filling. The self-induced mean field is a random spin-dependent potential. The energy of the spin-disordered state is shown to be lower than that of commensurate or incommensurate antiferromagnetic states. Long-wavelength charge and spin fluctuations obey the diffusion equation, leading to deviations from Fermi-liquid behavior. At wave vector q=(\ensuremath{\pi},\ensuremath{\pi}) the transverse spin-excitation spectrum has a gap.
We calculate the excitation spectrum and the response functions of the textures induced by doping in the half-filled Hubbard model. Localized states appear within the antiferromagnetic gap. The spin-wave spectrum is distorted, and shifted towards lower energies; its total strength is reduced. The antiferromagnetic peak at (\ensuremath{\pi},\ensuremath{\pi}) is broadened and moves to higher energies. Charge excitations appear at low energies and mix with the spin waves. Their polarization induces screened interactions that can overcome the initial, repulsive, ones. The general features of the results cannot be described in conventional-Fermi-liquid or, alternatively, insulator terms.
The magnetic states occurring in the two-dimensional Hubbard model in the vicinity of half-filling of the conduction band are studied in the case of weak correlations, using Hartree-Fock theory. It is shown that at zero temperature the commensurate antiferromagnetic state is unstable against domain-wall formation for arbitrarily small deviations from half-filling. The resulting incommensurate antiferromagnet remains initially insulating. The predictions of the model for the polarization and modulation wave vector of the incommensurate antiferromagnet are discussed.
We present fully self-consistent calculations in the fluctuation exchange approximation for the half-filled Hubbard model in two dimensions. A non-Fermi-liquid state evolves with decreasing temperature in this self-consistent model of coupled spin fluctuations and quasiparticles. The mean-field phase transition to long-range antiferromagnetic order is suppressed and we find no evidence of a phase transition to long-range magnetic order. We show that the real part of the self-energy at zero energy shows a positive slope and the imaginary part of the self-energy shows a local minimum. The scale of this structure is set by the zero-temperature gap in mean-field theory. The growth of spin fluctuations is reflected in the evolution of sharply peaked structure in the spin fluctuation propagator around zero energy and Q = (π, π). We present calculations for the Hubbard model in one dimension in a two-particle self-consistent parquet approximation. A second-moment sum rule suggests that vertex corrections to the self-energy are responsible for the greater accuracy of the parquet approximation compared with other self-consistent perturbation theories.
A two-dimensional square-lattice Hubbard model is investigated. A slave-fermion formulation, in which the electron operator is expressed by a combination of bose operators for the spin freedom, and fermi operators for the charge freedom, is used. The phase diagram for the resonating valence bond (RVB) state is obtained. The RVB state shows long-range antiferromagnetic order at T =0, the period of which deviates from that of the commensurate Néel order as the system deviates from the half-filled case.
Commensurate and incommensurate antiferromagnetic fluctuations in the two-dimensional repulsive $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}$-Hubbard model are investigated using functional renormalization group equations. For a sufficient deviation from half-filling we establish the existence of local incommensurate order below a pseudocritical temperature Tpc{T}_{pc}Tpc​. Fluctuations not accounted for in the mean-field approximation are important---they lower Tpc{T}_{pc}Tpc​ by a factor $\ensuremath{\approx}2.5$.