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arXiv:cond-mat/9802129

Destruction of Strong Critical Spin Fluctuations by Doping in the 2D Hubbard Model

Bumsoo Kyung

Published Feb 12, 1998• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.cond-mat/9802129

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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 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 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.
The effect of doping in the two-dimensional Hubbard model is studied within finite temperature exact diagonalization combined with cluster dynamical mean field theory. By employing a mixed basis involving cluster sites and bath molecular orbitals for the projection of the lattice Green's function onto 2x2 clusters, a considerably more accurate description of the low frequency properties of the self-energy is achieved than in a pure site picture. The transition from Fermi-liquid to non-Fermi-liquid behavior for decreasing hole doping is studied as a function of Coulomb energy, next-nearest neighbor hopping, and temperature. In particular, the self-energy component Sigma_X associated with X=(pi,0) is shown to exhibit an onset of non-Fermi-liquid behavior as the hole doping decreases below a critical value delta_c. The imaginary part of Sigma_X(omega) then develops a collective mode above E_F, which exhibits a distinct dispersion with doping. Accordingly, the real part of Sigma_X(omega) has a positive slope above E_F, giving rise to an increasing particle-hole asymmetry as the system approaches the Mott transition. This behavior is consistent with the removal of spectral weight from electron states close to E_F and the opening of a pseudogap which increases with decreasing doping. The phase diagram reveals that delta_c = 0.15 ... 0.20 for various system parameters. For electron doping, the collective mode of Sigma_X(omega) and the concomitant pseudogap are located below the Fermi energy which is consistent the removal of spectral weight from hole states just below E_F. The critical doping which marks the onset of non-Fermi-liquid behavior, is systematically smaller than for hole doping.
Electronic states in the two-dimensional Hubbard model are studied in the doped paramagnetic states by use of the auxiliary boson approach. Four auxiliary bosons are introduced by means of the Hubbard-Stratonovich transformation within the functional integral treatment. These bosons correspond to one charge and three spin fluctuations. An effective model is formulated. Going beyond the boson fluctuations around the saddle point, the single-electron Green's function including one-loop self-energy effects of fermion-boson interaction is derived. The behavior of the fermion self-energy, spectral functions, and density of states are investigated for several values of the Coulomb interaction UUU within the limit imposed by the Stoner criterion and also for small and moderate doping concentrations $\ensuremath{\delta}$. For small doping $(\ensuremath{\delta}=0.2)$, as UUU approaches a value determined by the Stoner criterion, the spin-boson spectrum has a striking low-energy enhancement around $\mathbf{q}\ensuremath{\sim}2{\mathbf{k}}_{F}.$ This enhancement of the spin fluctuation causes a non-Fermi-liquid-like low-energy $\ensuremath{\omega}$ linear dependence in the imaginary part of the self-energy. Due to the self-energy effects, band splittings and a band narrowing are produced in the spectral functions. As a consequence of this, the density of states has pseudogap structures around the quasiparticle band with a narrow bandwidth on the Fermi energy. These features seem to be precursors of the metal-insulator (Mott-Hubbard) transition and they might be related to the spin-gap phenomena observed in high-Tc{T}_{c}Tc​ materials. Our results for the density of states, the spectral function, and the band dispersions show qualitative agreement with the data of finite-size cluster simulations.
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.
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.