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 Letters

Exact demonstration of off-diagonal long-range order in the ground state of a Hubbard model

Shun-Qing Shen, Zhaoming Qiu

Published Dec 20, 1993• 59 citations
Publisher

Abstract

We present a rigorous proof that the ground state of a negative-U Hubbard model on some bipartite lattices \ensuremath{\Lambda} possesses off-diagonal long-range order in a finite range of the electron filling factor ${\mathrm{\ensuremath{\rho}}}_{\mathit{e}}$.

DOI
10.1103/physrevlett.71.4238

Related papers

Rigorous theorems on off-diagonal long-range order in the negative-UHubbard model

Guang-Shan Tian

In this article, we study off-diagonal long-range order in the negative-U Hubbard model. We rigorously prove that all the elements of the two-particle reduced density matrix are positive, which may indicate a Bose condensation at q=0. Furthermore, we shall show that the ground state at half filling has pseudospin number 0. It implies that a sufficient condition proposed by Yang and Zhang [Int. J. Mod. Phys. B 5, 977 (1991)], for a state \ensuremath{\Psi} having off-diagonal long-range order, may not be a necessary condition.

Physical review. B, Condensed matter•Feb 1, 1992•37 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

Ferrimagnetic long-range order of the Hubbard model

Shun-Qing Shen, Zhaoming Qiu, Guang-Shan Tian

In this paper, we show rigorously that there exists the ferrimagnetic long-range order in the ground state of the positive-U Hubbard model at half filling on some bipartite lattices. When ${\mathit{N}}_{\mathit{A}}$>${\mathit{N}}_{\mathit{B}}$(${\mathit{N}}_{\mathit{A}}$ and ${\mathit{N}}_{\mathit{B}}$ are the total site numbers of two sublattices A and B), except for the ferromagnetism which was found by Lieb [Phys. Rev. Lett. 62, 1201 (1989)], there also exists the antiferromagnetic long-range order in the ground state. This result only requires U>0 and is independent of the dimension of the lattices.

Physical Review Letters•Feb 21, 1994•85 citations

Two Theorems on the Hubbard-Hirsch Model

Wang Zhijun, Qiu Xiaoming

In this paper, the two theorems on the Hubbard–Hirsch model are shown rigorously. For positive on-site interaction , the model on some bipartite lattices has a weak ferromagnetic ground state at half filling. For negative , the ground state of the model on some bipartite lattices possesses off-diagonal long-range order within a finite range of the electron filling factor.

Communications in Theoretical Physics•Jul 30, 1997•9 citations

Investigation on the Ground State of the Hubbard Model

Gang Su, Mo‐Lin Ge

The absolute ground states of the Hubbard model are explicitly presented within the framework of pseudospin when and . It is shown that the states do not possess true off-diagonal long-range order in the two cases. It is also discovered that in the ground states the phase symmetry of the Hubbard model is spontaneously broken away from the half-filling, and the total spin is zero, which is independent of the sign of U and the electron filling in the considered periodic lattice.

Communications in Theoretical Physics•Jan 1, 1992•3 citations

Degeneracy of the ground states at half-filling and the existence of the η-pairing off-diagonal long-range order in the negative-U Hubbard models

Guang-Shan Tian

Solid State Communications•Jun 1, 1994•4 citations
We present a rigorous proof that the ground state of a negative-U Hubbard model on some bipartite lattices \ensuremath{\Lambda} possesses off-diagonal long-range order in a finite range of the electron filling factor \ensuremathρe{\mathrm{\ensuremath{\rho}}}_{\mathit{e}}\ensuremathρe​.
In this article, we study off-diagonal long-range order in the negative-U Hubbard model. We rigorously prove that all the elements of the two-particle reduced density matrix are positive, which may indicate a Bose condensation at q=0. Furthermore, we shall show that the ground state at half filling has pseudospin number 0. It implies that a sufficient condition proposed by Yang and Zhang [Int. J. Mod. Phys. B 5, 977 (1991)], for a state \ensuremath{\Psi} having off-diagonal long-range order, may not be a necessary condition.
In this paper, we show rigorously that there exists the ferrimagnetic long-range order in the ground state of the positive-U Hubbard model at half filling on some bipartite lattices. When NA{\mathit{N}}_{\mathit{A}}NA​>NB{\mathit{N}}_{\mathit{B}}NB​(NA{\mathit{N}}_{\mathit{A}}NA​ and NB{\mathit{N}}_{\mathit{B}}NB​ are the total site numbers of two sublattices A and B), except for the ferromagnetism which was found by Lieb [Phys. Rev. Lett. 62, 1201 (1989)], there also exists the antiferromagnetic long-range order in the ground state. This result only requires U>0 and is independent of the dimension of the lattices.