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Physical review. B, Condensed matter

Antiferromagnetic correlations in the two-dimensional Hubbard model

Bumsoo Kyung

Published Dec 15, 1998• 6 citations
Publisher

Abstract

We study the temperature and doping dependence of the two-dimensional (2D) Hubbard model in the intermediate coupling regime $(U=4).$ 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.

DOI
10.1103/physrevb.58.16032

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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 ∣Im\ensuremathΣ(kF,\ensuremathω)∣|\mathrm{Im}\ensuremath{\Sigma}({k}_{F},\ensuremath{\omega})|∣Im\ensuremathΣ(kF​,\ensuremathω)∣ at \ensuremathω=0,\ensuremath{\omega}=0,\ensuremathω=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 present strong numerical evidence for the band Kondo effect in the doped 2D Hubbard model by showing the systematic change of the density of states, imaginary part of the self-energy, effective magnetic moment and quasiparticle residue upon decreasing the temperature. Quadratically vanishing (in frequency) scattering rates near the Fermi energy and a linearly vanishing (in temperature) effective magnetic moment at low temperatures strongly support the screening of magnetic moments from singly occupied electrons by doped holes in the 2D Hubbard model.
We present the doping dependence of the spectral functions, density of states and low frequency behavior of the self-energy for the 2D Hubbard model on the basis of our recently developed theory for the Hubbard model. Strong 2D critical spin fluctuations dominating near half-filling are completely destroyed by 13 and 20 percent doping concentrations for U=4 and 8, respectively. Below these concentrations the imaginary part of the self-energy vanishes quadratically in frequency near the Fermi energy, a characteristic feature for the Fermi liquid.
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.
The influence of spin and charge fluctuations on spectra of the two-dimensional fermionic Hubbard model is considered using the strong coupling diagram technique. Infinite sequences of diagrams containing ladder inserts, which describe the interaction of electrons with these fluctuations, are summed, and obtained equations are self-consistently solved for the ranges of Hubbard repulsions [Formula: see text], temperatures [Formula: see text] and electron concentrations [Formula: see text] with t the intersite hopping constant. For all considered U the system exhibits a transition to the long-range antiferromagnetic order at [Formula: see text]. At the same time no indication of charge ordering is observed. Obtained solutions agree satisfactorily with results of other approaches and obey moments sum rules. In the considered region of the U-T plane, the curve separating metallic solutions passes from [Formula: see text] at the highest temperatures to U = 2t at [Formula: see text] for half-filling. If only short-range fluctuations are allowed for the remaining part of this region is occupied by insulating solutions. Taking into account long-range fluctuations leads to strengthening of maxima tails, which transform a part of insulating solutions into bad-metal states. For low T, obtained results allow us to trace the gradual transition from the regime of strong correlations with the pronounced four-band structure and well-defined Mott gap for [Formula: see text] to the Slater regime of weak correlations with the spectral intensity having a dip along the boundary of the magnetic Brillouin zone due to an antiferromagnetic ordering for [Formula: see text]. For [Formula: see text] and [Formula: see text] doping leads to the occurrence of a pseudogap near the Fermi level, which is a consequence of the splitting out of a narrow band from a Hubbard subband. Obtained spectra feature waterfalls and Fermi arcs, which are similar to those observed in hole-doped cuprates.
We study the finite-temperature Fermi-liquid to non-Fermi-liquid crossover in the two-dimensional Hubbard model for a range of dopings using the self-consistent ladder dual fermion method. We consider relatively high temperatures where by comparing the single-particle self-energy and the two-particle spin susceptibility we identify a suppression of the density of states near the Fermi level caused by a quasi-antiferromagnetic behavior that is itself characterized by a long, but finite, correlation length scale which we extract. We compute the single-particle self-energy, and the charge/spin susceptibilities for the entire doping range at relatively high temperature, and also for the half-filled weak-coupling case at relatively low temperatures. We perform fluctuation diagnostics to decompose the single-particle self-energy into scattering qqq-vector and bosonic frequency contributions in the spin channel. Within this framework we find that the key contributions to the single-particle self-energy that give non-Fermi-liquid character show complicated dependence on zero, positive, and negative frequency bosonic modes. We find that for a nominal choice of ${t}^{\ensuremath{'}}$ that electron- and hole-doped systems with similar Fermi-liquid character have distinct spin and charge susceptibility and distinct spin-fluctuation diagnostics spectra.