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The International Journal of High Performance Computing Applications

Quantum Monte Carlo Simulations of a CuO2 Model

Richard T. Scalettar, Douglas J. Scalapino, Robert L. Sugar, Steven R. White

Published Sep 1, 1991• 0 citations
Publisher

Abstract

The nature of the pairing mechanism responsible for high-temperature superconductivity remains a central theoretical puzzle in condensed matter physics. Here we discuss the properties of the two-dimensional CuO 2 layers common to these materials in terms of a three- band Hubbard model. We describe how recently devel oped quantum Monte Carlo simulation techniques al low one to calculate the physical properties of strongly interacting many-electron systems and discuss the re sources required for such simulations. Then we review what we have learned from these simulations about the antiferromagnetic, charge-transfer, and supercon ducting correlations in the three-band Hubbard model. We conclude with a discussion of future goals.

DOI
10.1177/109434209100500304

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In a recent Letter, Kuroki and Aoki [Phys. Rev. Lett. 76, 440 (1996)] presented quantum Monte-Carlo (QMC) results for pairing correlations in the three-band Hubbard model, which describes the Cu-d_{x^2-y^2} and O-p_{x,y} orbitals present in the CuO_2 planes of high-T_c materials. In this comment we argue that (i) the used parameter set is not appropriate for the description of high-T_c materials since it does not satisfy the minimal requirement of a charge-transfer gap at half-filling, and (ii) the observed increase in the d_{x^2-y^2} channel is dominantly produced by the pair-field correlations without the vertex part. Hence, the claim of evidence of ODLRO is not justified.

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The nature of the pairing mechanism responsible for high-temperature superconductivity remains a central theoretical puzzle in condensed matter physics. Here we discuss the properties of the two-dimensional CuO 2 layers common to these materials in terms of a three- band Hubbard model. We describe how recently devel oped quantum Monte Carlo simulation techniques al low one to calculate the physical properties of strongly interacting many-electron systems and discuss the re sources required for such simulations. Then we review what we have learned from these simulations about the antiferromagnetic, charge-transfer, and supercon ducting correlations in the three-band Hubbard model. We conclude with a discussion of future goals.
The nature of the pairing mechanism responsible for high-temperature superconductivity remains a central theoretical puzzle in condensed matter physics. In this paper the authors discuss the properties of the two-dimensional CuO{sub 2} layers common to these materials in terms of a three-bank Hubbard model. The authors describe how recently developed quantum Monte Carlo simulation techniques allow one to calculate the physical properties of strongly interacting many-electron systems and discuss the resources required for such simulations. Then the authors review what we have learned from these simulations about the antiferromagnetic, charge-transfer, and superconducting correlations in the three-band Hubbard model. The authors conclude with a discussion of future goals.
Theoretical ideas and experimental results concerning high-temperature superconductors are reviewed. Special emphasis is given to calculations performed with the help of computers applied to models of strongly correlated electrons proposed to describe the two-dimensional CuO2{\mathrm{O}}_{2}O2​ planes. The review also includes results using several analytical techniques. The one- and three-band Hubbard models and the $t\ensuremath{-}J$ model are discussed, and their behavior compared against experiments when available. The author found, among the conclusions of the review, that some experimentally observed unusual properties of the cuprates have a natural explanation through Hubbard-like models. In particular, abnormal features like the mid-infrared band of the optical conductivity $\ensuremath{\sigma}(\ensuremath{\omega})$, the new states observed in the gap in photoemission experiments, the behavior of the spin correlations with doping, and the presence of phase separation in the copper oxide superconductors may be explained, at least in part, by these models. Finally, the existence of superconductivity in Hubbard-like models is analyzed. Some aspects of the recently proposed ideas to describe the cuprates as having a ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ superconducting condensate at low temperatures are discussed. Numerical results favor this scenario over others. It is concluded that computational techniques provide a useful, unbiased tool for studying the difficult regime where electrons are strongly interacting, and that considerable progress can be achieved by comparing numerical results against analytical predictions for the properties of these models. Future directions of the active field of computational studies of correlated electrons are briefly discussed.
A possibility of the electronic origin of the high-temperature superconductivity in cuprates is probed with the quantum Monte Carlo method by revisiting the three-band Hubbard model comprising Cu ${3d}_{{x}^{2}{\ensuremath{-}y}^{2}}$ and O ${2p}_{\ensuremath{\sigma}}$ orbitals. The ${d}_{{x}^{2}{\ensuremath{-}y}^{2}}$ pairing correlation is found to turn into an increasing function of the repulsion Ud{U}_{d}Ud​ within the ddd orbitals or the ddd- ppp level offset $\ensuremath{\Delta}\ensuremath{\varepsilon}$, where the normalized correlation grows with the system size. We have detected this in both the charge-transfer and Mott-Hubbard regimes upon entering the strong-correlation region ( Ud{U}_{d}Ud​ or $\ensuremath{\Delta}\ensuremath{\varepsilon}>$ bare bandwidth).
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.
We study the three-band Hubbard model for the cuprate superconductors using Quantum Monte Carlo simulations and the fluctuation exchange approximation including a self-consistent many-body renormalization of the single-particle propagator. The energy dispersion of the low-lying one-particle excitations is in very good agreement with spectroscopic measurements for a hole doping concentration δ = 0.25 of the CuO2 planes. At the same doping, we examine the spin susceptibility yielding a non-ordered phase with short-range incommensurate fluctuations near the antiferromagnetic wave vector. In the superconducting regime, the interaction vertex for the pairing correlation function in the extended s-wave channel shows a maximum for δ = 0.20, resembling the dependence of transition temperature Tc on doping.
In a recent Letter, Kuroki and Aoki [Phys. Rev. Lett. 76, 440 (1996)] presented quantum Monte-Carlo (QMC) results for pairing correlations in the three-band Hubbard model, which describes the Cu-d_{x^2-y^2} and O-p_{x,y} orbitals present in the CuO_2 planes of high-T_c materials. In this comment we argue that (i) the used parameter set is not appropriate for the description of high-T_c materials since it does not satisfy the minimal requirement of a charge-transfer gap at half-filling, and (ii) the observed increase in the d_{x^2-y^2} channel is dominantly produced by the pair-field correlations without the vertex part. Hence, the claim of evidence of ODLRO is not justified.