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Journal de Physique I

Double layer Hubbard model : off-diagonal long range order in the nodeless d-wave channel

I. Morgenstern, Th. Hußlein, Johannes Maria Singer, Hans‐Georg Matuttis

Published Apr 1, 1993• 4 citations
Publisher

Abstract

We report on a numerical study of the double layer Hubbard model describing the CuO2 sheets in the high-Tc oxides. For the simulation we employed the projector quantum Monte Carlo method (PQMC) to study the ground state properties of this correlated electron system. Our results provide evidence for off-diagonal long range order in the nodeless d-wave channel. The implications with respect to possible mechanisms for high-Tc superconductivity in oxides in combination which phononic booster mechanisms are discussed.

DOI
10.1051/jp1:1993109

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We report on a numerical study of the double layer Hubbard model describing the CuO2 sheets in the high-Tc oxides. For the simulation we employed the projector quantum Monte Carlo method (PQMC) to study the ground state properties of this correlated electron system. Our results provide evidence for off-diagonal long range order in the nodeless d-wave channel. The implications with respect to possible mechanisms for high-Tc superconductivity in oxides in combination which phononic booster mechanisms are discussed.
We have carried out Quantum Monte Carlo studies to investigate the double layer Hubbard model using the groundstate projector formalism. Evidence for off diagonal long range order in the nodeless d-wave pairing channel is provided. It is emphasized that the Projector Quantum Monte Carlo method has the potential to detect superconducting mechanisms in strongly correlated electron systems, which are not treatable by standard analytic methods. The Monte Carlo technique provides useful information about systems much larger than those accessible for exact diagonalization methods.
We study a model for high- T c superconductors describing both the strong electronic correlations and a coupling of the carriers to anharmonic phonons. The Projector Quantum Monte Carlo Scheme has been employed to investigate ground state properties. We analyze the superconducting properties of the model by directly addressing to the existence of Off-Diagonal Long Range Order (ODLRO). We review the numerical algorithm and discuss the possibility to observe ODLRO. In the presented model, we find ODLRO pointing towards superconductivity instead of the presence of strong electronic correlations. We discuss several features of the superconducting condensate.
Superconducting properties of coupled Hubbard planes are studied by quantum Monte Carlo simulations. It is found that the interlayer coupling supports the pairing mechanism but it does not lead to off-diagonal long-range order in the purely electronic system. In addition, we have performed Monte Carlo studies based on a recently proposed variational wave function. Yielding identical results, the variational wave function overcomes the sign problem and allows us to analyze ground-state properties of strongly correlated many-body problems for system sizes and complexities not accessible otherwise.
We investigate the ground-state properties of the two-dimensional Hubbard model, based on the off-diagonal wave function variational Monte Carlo method. We use an optimized wave function that is improved from an initial one-body wave function by multiplying by multiple correlation operators that are given by the form of exp(−S-S−S)-type where SSS is a suitable operator. We examine the inhomogeneous ground state at near 1/8 doping in the strongly correlated region where the on-site Coulomb interaction is larger than the bandwidth. The ddd-wave superconductivity with a spatially oscillating gap function can coexist with the charge ordering in the ground state without magnetic ordering, and superconducting condensation energy increases by this coexistence. We also show the ddd-wave pair correlation function as a function of lattice sites. The correlation function indicates that the long-range superconducting order indeed exists, and also that the strong electron correlation suppresses the pair correlation function.
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.
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.