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International Journal of Modern Physics B

PRECURSOR OF ANTIFERROMAGNETIC BANDS IN THE HALF-FILLED TWO-DIMENSIONAL HUBBARD MODEL

Bumsoo Kyung

Published Oct 30, 1999• 0 citations
Publisher

Abstract

We study the half-filled two-dimensional Hubbard model in the intermediate coupling regime. As temperature is decreased for a two-dimensional half-filled band, two-dimensional critical fluctuations give rise to a strong local maximum in | Im Σ(k F , ω)| at ω=0, leading to a split peak with a pseudogap inside in the spectral function and the density of states. The calculated energy dispersion is in good agreement with that of spin density wave approximation.

DOI
10.1142/s0217979299002940

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We study the half-filled two-dimensional Hubbard model in the intermediate coupling regime. As temperature is decreased for a two-dimensional half-filled band, two-dimensional critical fluctuations give rise to a strong local maximum in | Im Σ(k F , ω)| at ω=0, leading to a split peak with a pseudogap inside in the spectral function and the density of states. The calculated energy dispersion is in good agreement with that of spin density wave approximation.
We study the temperature and doping dependence of the two-dimensional (2D) Hubbard model in the intermediate coupling regime (U=4).(U=4).(U=4). As temperature is decreased for a half-filled band, 2D critical spin fluctuations give rise to a strong local maximum in $|\mathrm{Im}\ensuremath{\Sigma}({k}_{F},\ensuremath{\omega})|$ at $\ensuremath{\omega}=0,$ leading to a split peak in the spectral function. These strong fluctuations dominating near half filling are completely destroyed by 12% doping concentration. Below this concentration the imaginary part of the self-energy vanishes nearly quadratically in frequency at the Fermi energy, a Fermi-liquid-like feature. With varying the temperature at this concentration, we present numerical evidence for the band Kondo effect in the doped 2D Hubbard model by showing at low temperatures a growing peak in the density of states, nearly quadratically vanishing (in frequency) scattering rates at the Fermi energy and a linearly vanishing (in temperature) effective magnetic moment.
We formulate a theory to the 2D Hubbard model in a framework free of finite size effect and numerical analytical continuation, yet containing the essential features of the 2D Hubbard model, i.e., the correct atomic limit for large frequencies and 2D spin fluctuations. As temperature is decreased for a 2D half-filled band, 2D critical fluctuations give rise to a strong local maximum in the scattering rates at the chemical potential leading to a split peak in the spectral function. As U is increased, four peaks associated with antiferromagnetic and Hubbard bands begin to develop in small and intermediate frequency regimes.
Starting from the Hubbard model in the weak-coupling limit, we derive a spin-fermion model where the collective spin excitations are described by a nonlinear sigma model. This result is used to compute the fermion spectral function $A(\mathbf{k},\ensuremath{\omega})$ in the low-temperature regime where the antiferromagnetic (AF) coherence length is exponentially large (``renormalized classical'' regime). At the Fermi level, $A({\mathbf{k}}_{F},\ensuremath{\omega})$ exhibits two peaks around $\ifmmode\pm\else\textpm\fi{}{\ensuremath{\Delta}}_{0}$ (with ${\ensuremath{\Delta}}_{0}$ the mean-field gap), which are precursors of the zero-temperature AF bands, separated by a pseudogap.
We have studied the pseudogap formation in the single-particle spectra of the half-filling two-dimensional Hubbard model. Using a Green's function with the one-loop self-energy correction of the spin and charge fluctuations, we have numerically calculated the self-energy, the spectral function, and the density of states in the weak-coupling regime at finite temperatures. Pseudogap formations have been observed in both the density of states and the spectral function at the Fermi level. The pseudogap in the spectral function is explained by the non-Fermi-liquid-like nature of the self-energy. The anomalous behavior in the self-energy is caused by both the strong antiferromagnetic spin fluctuation and the nesting condition on the non-interacting Fermi surface. In the present approximation, we find a logarithmic singularity in the integrand of the self-energy imaginary part. The pseudogap in the spectral function is highly momentum dependent on the Fermi surface. This anisotropy of the pseudogap is produced by the flatness of the band dispersion around the saddle point rather than the nesting condition on the Fermi level.
We present single-particle and thermodynamic properties of the half-filled single-band Hubbard model in 2D calculated in the self-consistent fluctuation exchange approximation. The low-energy excitations at moderate temperatures and small UUU are quasiparticles with a short lifetime. As the temperature is lowered, coupling to evolving spin fluctuations leads to the extinction of these quasiparticles, signaled by a weak pseudogap in the density of states and by a positive slope in $\mathrm{Re}\ensuremath{\Sigma}({\mathbf{k}}_{F},\ensuremath{\varepsilon})$ and a local maximum in $|\mathrm{Im}\ensuremath{\Sigma}({\mathbf{k}}_{F},\ensuremath{\varepsilon})|$ at $\ensuremath{\varepsilon}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$. We explain these results using a simple spin-fluctuation model.
Using quantum Monte Carlo, we study the evolution of pseudogaps in the spectral weight function for a half-filled two-dimensional Hubbard model as a function of temperature and coupling constant. The formation of pseudogaps at finite temperature can be used to distinguish between three regimes: (1) a strong-coupling Mott-Hubbard regime, characterized by a pseudogap which persists even at high temperatures; (2) a weak-coupling spin-density-wave regime, characterized by the absence of a pseudogap at any finite temperature; and (3) an intermediate-coupling regime with mixed behavior, characterized by a pseudogap that appears at a finite temperature.