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International Journal of Modern Physics C

OFF-DIAGONAL LONG RANGE ORDER IN AN ELECTRON-PHONON MODEL FOR HIGH- T c SUPERCONDUCTORS

M. Frick, I. Morgenstern, Wolfgang von der Linden

Published Feb 1, 1992• 4 citations
Publisher

Abstract

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.

DOI
10.1142/s0129183192000099

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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.
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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 show that in the translation invariant case and in the antiferromagnetic phase, the reduced density matrix ρ2 has no off-diagonal long-range order of on-site electron pairs for the single-band Hubbard model on a cubic lattice away from half filling at finite temperatures both for the positive coupling and for the negative coupling. In these cases the model can not give a mechanism for the superconductivity caused by the condensation of on-site electron pairs and the nearestneighbor electron pairs. PACS numbers: 71.10.+x, 74.20.-z, 05.30.-d. 1 It was proposed the possibility that the Hubbard model can give a mechanism to characterize high temperature superconductivity[1]. It has been shown that the η pairing states for the single band Hubbard model with constant hopping matrix element for nearest neighbor sites have ODLRO[2]. It has also been shown that in the ground state the model with negative coupling has off-diagonal long-range order (ODLRO) on some bipartite lattice[3]. However, as the temperature T> 0 whether the reduced density matrix ρ2 has ODLRO is inconclusive. The purpose of this work is to study the ODLRO of ρ2 in the single-band Hubbard model with constant hopping matrix element for nearest neighbor pairs on a cubic lattice at finite temperatures. In the translation invariant case we obtain an equation ( (10) in the following) which is satisfied by the long-range correlation functions of on-site electron pairs. From which we find that there is no ODLRO of on-site electron pairs. Then we consider the case with an antiferromagnetic background. In this case we will show that there is still no ODLRO of on-site electron pairs. The Hamiltonian of the model is H = −t ∑ (a † rar ′ + b † rb ∑
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.
For a strongly interacting boson system, it has been proposed that the concept of off-diagonal long-range ordering (ODLRO) is equivalent to Bose-Einstein condensation for a free boson system. Therefore, the existence of ODLRO in the ground state implies superfluidity. The author checks the validity of this proposition from another point of view. He rigorously shows that, for a hard-core lattice-boson system with a short-ranged interaction ODLRO is suppressed when a charged excitation gap develops and, hence, the boson system becomes a Mott-insulator. Finally, by using his theorem, he shows some interesting properties of the antiferromagnetic Heisenberg model, which can be taken as a hard-core lattice-boson system.