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Europhysics Letters (EPL)

Spin and Charge Excitations Induced by Holes in the Hubbard Model

F. Guinea, Enrique Louis, José Antonio Vergés

Published Feb 1, 1992• 8 citations
Publisher

Abstract

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 shifted to lower frequencies, although the antiferromagnetic peak at zero energy is depleted. Charge excitations appear at energies comparable to the spin modes. These excitations mediate effective interactions which can be attractive for next-nearest-neighbour sites. The overall features of the results are inconsistent with normal metal behaviour, as described by the same scheme.

DOI
10.1209/0295-5075/17/5/013

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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 shifted to lower frequencies, although the antiferromagnetic peak at zero energy is depleted. Charge excitations appear at energies comparable to the spin modes. These excitations mediate effective interactions which can be attractive for next-nearest-neighbour sites. The overall features of the results are inconsistent with normal metal behaviour, as described by the same scheme.
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.
We study the one-dimensional extended Hubbard model with alternating size of the hopping integrals using the density-matrix renormalization group method. We calculate the spin gap, the Tomonaga-Luttinger parameter, and the charge-density-wave order parameter for various dimerizations, interaction strengths, and band fillings. At half band-filling the spin and charge excitations are gapped but these gaps disappear for infinitesimal hole doping. At quarter filling, the umklapp scattering in the half-filled lower Peierls band generates a gap for the charge excitations but the gapless spin excitations can be described in terms of an effective antiferromagnetic Heisenberg model. Beyond a critical strength for the nearest-neighbor interaction, the dimerized extended Hubbard model at quarter filling develops a charge-density-wave ground state. The dimerization and the nearest-neighbor Coulomb interaction strongly reduce the Tomonaga-Luttinger parameter from its value for the bare Hubbard model. We discuss the relevance of our findings for the Bechgaard salts.
We determine the spin and charge orders in the ground state of the doped two-dimensional (2D) Hubbard model in its simplest form, namely with only nearest-neighbor hopping and on-site repulsion. At half-filling, the ground state is known to be an antiferromagnetic Mott insulator. Doping Mott insulators is believed to be relevant to the superconductivity observed in cuprates. A variety of candidates have been proposed for the ground state of the doped 2D Hubbard model. A recent work employing a combination of several state-of-the-art numerical many-body methods established the stripe order as the ground state near 1/81/81/8 doping at strong interactions. In this paper, we apply one of these methods, the cutting-edge constrained-path auxiliary field quantum Monte Carlo (AFQMC) method with self-consistently optimized gauge constraints, to systematically study the model as a function of doping and interaction strength. With careful finite size scaling based on large-scale computations, we map out the ground state phase diagram in terms of its spin and charge order. We find that modulated antiferromagnetic order persists from near half-filling to about 1/51/51/5 doping. At lower interaction strengths or larger doping, these ordered states are best described as spin-density waves, with essentially delocalized holes and modest oscillations in charge correlations. When the charge correlations are stronger (large interaction or small doping), they are best described as stripe states, with the holes more localized near the node in the antiferromagnetic spin order. In both cases, we find that the wavelength in the charge correlations is consistent with so-called filled stripes.
The applicability of the Hartree-Fock and random phase approximations to models of strongly correlated electrons is discussed. The 2D Hubbard model is analyzed. An antiferromagnetic phase (at half filling) and Fermi liquid behavior (at low electron densities) are found. In addition, the system shows an unconventional regime near half filling. It is characterized by the formation of spin and charge textures. Local magnetic moments and spin waves are also present, and the quasiparticle pole at the Fermi energy vanishes. The charge excitation spectrum is gapless. The overall features resemble those of the 1D Luttinger liquid.
We study the extended Hubbard model on a two-dimensional half-filled square lattice using the dynamical cluster approximation. We present results on the phase boundaries between the paramagnetic metallic (normal) state and the insulating antiferromagnetic state, as well as between the antiferromagnetic and charge-order states. We find hysteresis along the antiferromagnet/charge order and normal/charge-order phase boundaries (at larger values of the on-site interaction), indicating first-order phase transitions. We show that nearest-neighbor interactions lower the critical temperature for the antiferromagnetic phase. We also present results for the effect of nearest-neighbor interactions on the antiferromagnetic phase boundary and for the evolution of spectral functions and energetics across the phase transitions.
We study the effects of doping on the spin fluctuations of the two-dimensional Hubbard model. Within a harmonic approximation we calculate the linearized antiferromagnetic spin-wave spectra around a hole away from half-filling, which takes the form of a spin polaron in a mean-field approximation. The presence of the spin polaron breaks a symmetry of the problem, the product of time reversal and lattice translation. As a result, the double degeneracy of the magnon spectra of the N\'eel state is lifted. There also appear localized magnon modes depending on the ratio U/t of the Hubbard model. The quantum correction due to the spin fluctuations is found to increase the spin polaron binding energy for U/t13, but decreases it for U/t>13.