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Physical review. B, Condensed matter

Spin and charge dynamics in a one-dimensional two-band Hubbard model

Hong Q. Ding, William A. Goddard

Published Jan 1, 1993• 4 citations
Publisher

Abstract

A CuO chain with one or two holes doped is studied via the two-band Hubbard model in the large-U limit on a finite cluster. The quasiparticle band is ${\mathit{E}}_{\mathit{k}}$\ensuremath{\sim}0.87J cos(2ka) with the bottom at ka=\ensuremath{\pi}/2. The quasiparticles are kinks which have the character of three-spin polarons. The copper spin excitations are incommensurate spin waves. The two doped holes repel each other very slightly, in contrast to the slight attraction in the t-J model. Spin-charge separation also occurs.

DOI
10.1103/physrevb.47.1149

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A CuO chain with one or two holes doped is studied via the two-band Hubbard model in the large-U limit on a finite cluster. The quasiparticle band is Ek{\mathit{E}}_{\mathit{k}}Ek​\ensuremath{\sim}0.87J cos(2ka) with the bottom at ka=\ensuremath{\pi}/2. The quasiparticles are kinks which have the character of three-spin polarons. The copper spin excitations are incommensurate spin waves. The two doped holes repel each other very slightly, in contrast to the slight attraction in the t-J model. Spin-charge separation also occurs.
A single hole doped into the CuO2{\mathrm{CuO}}_{2}CuO2​ plane of a high-Tc{\mathit{T}}_{\mathit{c}}Tc​ superconductor is studied via exact calculations of the three-band Hubbard model (large-U limit) on a 4\ifmmode\times\else\texttimes\fi{}4 periodic cluster. The quasiparticle band has its bottom at k=(\ensuremath{\pi}/2,\ensuremath{\pi}/2) and disperses strongly towards \ensuremath{\Gamma} and X with a dispersion 1.7Jdd{\mathit{J}}_{\mathit{d}\mathit{d}}Jdd​=0.22 eV. The quasiparticle has a nearly isotropic effective mass (\ensuremath{\sim}4me{\mathit{m}}_{\mathit{e}}me​) and the dressing effects are well localized (\ensuremath{\sim}8 \AA{}) with characteristic features of both the three-spin polaron and the Zhang-Rice singlet (although solutions of the t-J model are substantially different).
We extend the methods recently introduced [Phys. Rev. Lett. 106, 036401 (2011)] to investigate correlations between two spin-polarons in a quasi-two-dimensional CuO2{}_{2}2​ layer. The low-energy wave functions for two doped holes introduced in a half filled CuO2{}_{2}2​ plane with 32 copper and 64 oxygen sites are calculated explicitly using an efficient yet accurate truncation scheme to model the antiferromagnet background. The energetics and wave functions show that the charges form three spin-polarons and the spin is carried by a disturbance around the three spin-polaron core. The low-energy band results from the competition between the kinetic energy and a local attractive potential, which favors ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ states. Last, we point out features that are expected to be robust for larger systems.
A one-dimensional two-band Hubbard model describing CuO chains is considered in the limit of zero bandwidth. Onsite and nearest-neighbor Coulomb interactions are included in the description. Various density correlation functions are calculated exactly at arbitrary concentration of holes. For increasing values of the intersite Coulomb interaction V, the system is driven towards both a charge-transfer instability and a phase separation instability when doped away from half filling. In the case of one hole added to the half-filled system, it is shown that a hole binds to a biexciton. Three-body bound states recently proposed to produce the marginal Fermi-liquid spectrum also occur naturally in the model, but a finite amount of doping away from half filling is necessary for them to form to an appreciable extent in the thermodynamic limit.
The one-dimensional three-band Hubbard Hamiltonian is shown to be equivalent to an effective Hamiltonian that has independent spinon and holon quasiparticle excitations plus a weak coupling of the two. The spinon description includes both copper sites and oxygen hole sites leading to a one-dimensional antiferromagnet incommensurate with the copper lattice. The holons are spinless noninteracting fermions in a simple cosine band. Because the oxygen sites are in the Hamiltonian, the quasiparticles are much simpler than in the exact solution of the t-J model for 2t = +/- J. If a similar description is correct for two dimensions, then the holons will attract in a p-wave potential.
The question of spin-charge separation in two-dimensional lattices has been addressed by numerical simulations of the motion of one hole in a half-filled band. The calculations have been performed on finite clusters with Hubbard and t-J models. By comparing the time evolution of spin and charge polarization currents in one and two dimensions, evidence in favor of spin-charge separation in two dimensions is presented. In contrast with this, spin-charge separation is absent in a highly doped, metallic, system.
A two-band Hubbard model describing a CuO chain is studied using quantum Monte Carlo simulation. The Luttinger-liquid exponent K ρ is extracted as a function of the nearest-neighbor repulsion V , at hole fillings ⟨ n ⟩ between 1 (half-filled lower band) and 2. Evidence is presented for the existence of a regime with dominant singlet superconducting fluctuations and a gap in the spin excitation spectrum at ⟨ n ⟩ = 1.75, in the neighborhood of the V for which the system phase separates. Closer to half-filling (⟨ n ⟩≲1.6), spin-density-wave fluctuations always dominate.