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arXiv:cond-mat/0309050 · Physical Review B

Friedel oscillations in a two-band Hubbard model for CuO chains

Masakatsu Mori, Takami Tohyama, Sadamichi Maekawa, José A. Riera

Published Jan 28, 2004• 5 citations
arXivHTMLPDF

Abstract

Friedel oscillations induced by open boundary conditions in a two-band Hubbard model for CuO chains are numerically studied. We find that for physically realistic parameters and close to quarter filling, these oscillations have a ${2k}_{F}$ modulation according with experimental results on ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}.$ In addition, we predict that, for the same parameters, as hole doping is reduced from quarter filling to half filling, Friedel oscillations would acquire a ${4k}_{F}$ modulation, typical of a strongly correlated electron regime. The ${4k}_{F}$ modulation also dominates in the electron doped region. The range of parameters varied is very broad, and hence the results reported could apply to other cuprates and other strongly correlated compounds with quasi-one-dimensional structures. On a more theoretical side, we stress the fact that the copper and oxygen subsystems should be described by two different Luttinger liquid exponents.

DOI
10.1103/physrevb.69.014513

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Friedel oscillations induced by open boundary conditions in a two-band Hubbard model for CuO chains are numerically studied. We find that for physically realistic parameters and close to quarter filling, these oscillations have a 2kF{2k}_{F}2kF​ modulation according with experimental results on YBa2Cu3O7\ensuremath−\ensuremathδ.{\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}.YBa2​Cu3​O7\ensuremath−\ensuremathδ​. In addition, we predict that, for the same parameters, as hole doping is reduced from quarter filling to half filling, Friedel oscillations would acquire a 4kF{4k}_{F}4kF​ modulation, typical of a strongly correlated electron regime. The 4kF{4k}_{F}4kF​ modulation also dominates in the electron doped region. The range of parameters varied is very broad, and hence the results reported could apply to other cuprates and other strongly correlated compounds with quasi-one-dimensional structures. On a more theoretical side, we stress the fact that the copper and oxygen subsystems should be described by two different Luttinger liquid exponents.
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.
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.
The phase-separation instability occurring with increasing nearest-neighbor repulsion VVV in a two-band Hubbard model (CuO chain) is discussed. Quantum Monte Carlo simulations indicate that this transition is strongly discontinuous if the filling fraction 〈n〉〈n〉〈n〉 is close to 1 (half-filled lower band). Spin-density-wave fluctuations then dominate before phase separation. Superconducting fluctuations dominate in the neighborhood of phase separation only at considerably higher doping levels, where the transition to the phase-separated state is much smoother.
We present recent theoretical results on superconductivity in correlated-electron systems, especially in the two-dimensional Hubbard model and the three-band d-p model. The mechanism of superconductivity in high-temperature superconductors has been extensively studied on the basis of various electronic models and also electron-phonon models. In this study, we investigate the properties of superconductivity in correlated-electron systems by using numerical methods such as the variational Monte Carlo method and the quantum Monte Carlomethod. The Hubbard model is one of basic models for strongly correlated electron systems, and is regarded as the model of cuprate high temperature superconductors. The d-p model is more realistic model for cuprates. The superconducting condensation energy obtained by adopting the Gutzwiller ansatz is in reasonable agreement with the condensation energy estimated for YBa2Cu3O7. We show the phase diagram of the ground state using this method. We have further investigated the stability of striped and checkerboard states in the under-doped region. Holes doped in a half-filled square lattice lead to an incommensurate spin and charge density wave. The relationship of the hole density x and incommensurability δ, δ~x, is satisfied in the lower doping region, as indicated by the variationalMonte Carlocalculations for the two-dimensional Hubbard model. A checkerboard-like charge-density modulation with a roughly period has also been observed by scanning tunneling microscopy experiments in Bi2212 and Na-CCOC compounds. We have performed a variational Monte Carlo simulation on a two-dimensional t-t′-t″- U Hubbard model with a Bi-2212 type band structure and found that the period checkerboard spin modulation, that is characterized by multi Q vectors, is indeed stabilized. We have further performed an investigation by using a quantumMonte Carlomethod, which is a numerical method that can be used to simulate the behavior of correlated electron systems. We present a new algorithm of the quantum Monte Carlo diagonalization that is a method for the evaluation of expectation value without the negative sign problem. We compute pair correlation functions and show that pair correlation is indeed enhanced with hole doping.
On the basis of exact diagonalizations, a comparative study of two-particle optical and magnetic, as well as single-particle, excitations is presented for a two-dimensional (2D) multiorbital Hubbard model. For reasonable parameter sets appropriate for the cuprate superconductors, the single-particle excitations display strongly correlated states related to the Zhang-Rice Cu-O singlet construction. These states define the gap (to the upper Hubbard band) at half-filling and become partially occupied by doping holes in our 2\ifmmode\times\else\texttimes\fi{}2 unit-cell system. The optical results, which are the first quantitative calculations performed for realistic parameters of the three-band Hubbard model, clearly show three allowed optical transitions: (i) itinerant motion of the Cu-O singlets, having (for doping concentrations x\ensuremath{\ne}0) a spectral Drude distribution around \ensuremath{\omega}=0 with spectral weight proportional to x; (ii) unbinding of the O hole from the Cu spin in the singlet. This gives, in particular, a strong absorption peak due to singlet\ensuremath{\rightarrow}nonbonding oxygen transitions, again with relative weight \ensuremath{\sim}x.It is roughly centered at \ensuremath{\omega}\ensuremath{\sim}JKondo{\mathit{J}}_{\mathrm{Kondo}}JKondo​, where JKondo{\mathit{J}}_{\mathrm{Kondo}}JKondo​ is the Kondo coupling and \ensuremath{\Delta} the bare Cu-O charge-transfer energy. It is this singlet unbinding that results in the by far dominant absorption structure between Drude and higher-energy Cu-O transitions and not the often discussed ``mid-infrared'' absorption due to transitions between different singlet states. (iii) Cu-O charge-transfer processes at energy \ensuremath{\sim}\ensuremath{\Delta}+Upd{\mathit{U}}_{\mathit{p}\mathit{d}}Upd​. They show a pronounced excitonic effect due to the p-d interaction Upd{\mathit{U}}_{\mathit{p}\mathit{d}}Upd​ and have a reduced spectral weight shifted to higher energies for increased dopings. Findings (i)--(iii) are in general accordance with recent experimental data. Our study of the low-energy absorption is complemented with a numerical scaling analysis of the Drude weight in 1D, where, in particular, we find an interesting violation of Lenz's law for 4n-site Hubbard rings. Finally, the magnetic structure factor is calculated for the 2D case. For finite doping it contains a peak at 2JKondo{\mathit{J}}_{\mathrm{Kondo}}JKondo​, which should be detectable in experiment.
Using the density-matrix renormalization-group (DMRG) technique, we calculate critical exponents for the one-dimensional Hubbard model with open boundary conditions with and without additional boundary potentials at both ends. A direct comparison with open boundary condition Bethe ansatz calculations provides a good check for the DMRG calculations on large system sizes. On the other hand, the DMRG calculations provide an independent check of the predictions of conformal field theory, which are needed to obtain the critical exponents from the Bethe ansatz. From the Bethe ansatz we predict the behavior of the 1/L1/L1/L-corrected mean value of the Friedel oscillations (for the density and the magnetization) and the characteristic wave vectors, and show numerically that these conjectures are fulfilled with and without boundary potentials. The quality of the numerical results allows us to determine the behavior of the coefficients of the Friedel oscillations as a function of the Hubbard interaction.