Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical review. B, Condensed matter

Ground-state BCS off-diagonal long-range order in one dimension

Richard M. Fye

Published Jan 1, 1993• 1 citation
Publisher

Abstract

We prove the existence of ground-state BCS off-diagonal long-range order (ODLRO) in a nontrivial interacting-electron model of dimension d=1. Somewhat surprisingly, the BCS ODLRO is induced here by a magnetic field. Our existence results extend to all dimensions (d\ensuremath{\ge}1) recent work that proved the existence of BCS ODLRO in nontrivial interacting-electron models for dimensions d\ensuremath{\ge}2.

DOI
10.1103/physrevb.47.1113

Related papers

Off-Diagonal Long-Range Order in Generalized Hubbard Models

Kristel F. L. Michielsen, Hans A. De Raedt

We present stochastic diagonalization results for the ground-state energy and the largest eigenvalue of the two-fermion density matrix of the BCS reduced Hamiltonian, the Hubbard model, and the Hubbard model with correlated hopping. The system-size dependence of this eigenvalue is used to study the existence of Off-Diagonal Long-Range Order in these models. We show that the model with correlated hopping and repulsive on-site interaction can exhibit Off-Diagonal Long-Range Order. Analytical results for some special limiting cases indicate that Off-Diagonal Long-Range Order not always implies superconductivity.

International Journal of Modern Physics B•May 10, 1997•10 citations

Rigorous eta -pairing ground state in an extended Hubbard model

Z J Wang, X M Qiu, Xingjiang Zhou

In this paper we show the existence of eta -pairing and off-diagonal long-range order (ODLRO) in the ground state of an extended Hubbard model with N up arrow -N down arrow =1, where N up arrow and N down arrow are the occupation numbers of up and down spins, for connected bipartite lattices.

Journal of Physics A Mathematical and General•Jun 21, 1995•0 citations

A rigorous theorem on off-diagonal long-range order of boson systems

Guang-Shan Tian

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.

Journal of Physics A Mathematical and General•May 21, 1992•5 citations

Long-Range Order in Ideal Ferromagnets

Masuo Suzuki

An attempt is made to investigate the relation between (diagonal) long-range order (LRO or spontaneous magnetization in spin systems) and off-diagonal long-range order (ODLRO or long-range correlation in spin systems). It is shown that ODLRO cannot exceed LRO in ideal ferromagnets under some plausible conditions. Several kinds of long-range order and their mutual relations are also discussed in ideal ferromagnets whose total spin commutes with the Hamiltonian. It is also argued that neither LRO or ordinary ODLRO exists in the two-dimensional ferromagnetic Heisenberg model. However, a possibility is proposed that other kinds of ODLRO exist in the case of higher spin for such a system. The Heisenberg model with long-range interaction is exemplified, and it is pointed out that the total spin, instead of the total magnetization, should be taken as an order parameter in phenomenological arguments of the Heisenberg model.

Progress of Theoretical Physics•Nov 1, 1969•12 citations

New Types of Off-Diagonal Long Range Order in Quantum Spin Chains

J. C. Talstra, Steven P. Strong, P. W. Anderson

We discuss new possibilities for off-diagonal long range order (ODLRO) in spin chains involving operators which add or delete sites from the chain. For the one-dimensional, periodic Heisenberg, inverse square exchange, and $\mathrm{XY}$ models we give numerical evidence for the hidden ODLRO conjectured by Anderson. A connection to the singlet pair correlations in one-dimensional models of interacting electrons is made and briefly discussed.

arXiv:cond-mat/9411074•Physical Review Letters•Jun 26, 1995•21 citations

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

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

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.

International Journal of Modern Physics C•Feb 1, 1992•4 citations
We prove the existence of ground-state BCS off-diagonal long-range order (ODLRO) in a nontrivial interacting-electron model of dimension d=1. Somewhat surprisingly, the BCS ODLRO is induced here by a magnetic field. Our existence results extend to all dimensions (d\ensuremath{\ge}1) recent work that proved the existence of BCS ODLRO in nontrivial interacting-electron models for dimensions d\ensuremath{\ge}2.
We present stochastic diagonalization results for the ground-state energy and the largest eigenvalue of the two-fermion density matrix of the BCS reduced Hamiltonian, the Hubbard model, and the Hubbard model with correlated hopping. The system-size dependence of this eigenvalue is used to study the existence of Off-Diagonal Long-Range Order in these models. We show that the model with correlated hopping and repulsive on-site interaction can exhibit Off-Diagonal Long-Range Order. Analytical results for some special limiting cases indicate that Off-Diagonal Long-Range Order not always implies superconductivity.
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.
An attempt is made to investigate the relation between (diagonal) long-range order (LRO or spontaneous magnetization in spin systems) and off-diagonal long-range order (ODLRO or long-range correlation in spin systems). It is shown that ODLRO cannot exceed LRO in ideal ferromagnets under some plausible conditions. Several kinds of long-range order and their mutual relations are also discussed in ideal ferromagnets whose total spin commutes with the Hamiltonian. It is also argued that neither LRO or ordinary ODLRO exists in the two-dimensional ferromagnetic Heisenberg model. However, a possibility is proposed that other kinds of ODLRO exist in the case of higher spin for such a system. The Heisenberg model with long-range interaction is exemplified, and it is pointed out that the total spin, instead of the total magnetization, should be taken as an order parameter in phenomenological arguments of the Heisenberg model.
We discuss new possibilities for off-diagonal long range order (ODLRO) in spin chains involving operators which add or delete sites from the chain. For the one-dimensional, periodic Heisenberg, inverse square exchange, and XY\mathrm{XY}XY models we give numerical evidence for the hidden ODLRO conjectured by Anderson. A connection to the singlet pair correlations in one-dimensional models of interacting electrons is made and briefly discussed.
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.