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 resonating-valence-bond ground state and possibility of superconductivity in repulsive Hubbard models

Hal Tasaki

Published May 24, 1993• 18 citations
Publisher

Abstract

We generalize the exactly solvable Hubbard model with infinitely large on-site Coulomb repulsion recently introduced by Brandt and Giesekus. We point out that the exact ground state can be regarded as a resonating-valence-bond state, and argue that the state may exhibit superconductivity. The existence of a phase with singlet-pair ordering is demonstrated in a simple model on a tree.

DOI
10.1103/physrevlett.70.3303

Related papers

A model of strongly correlated electrons with condensed resonating-valence-bond ground states

Akinori Tanaka

We propose a new exactly solvable model of strongly correlated electrons. The model is based on a d – p model of the CuO 2 plane with infinitely large repulsive interactions on Cu-sites, and it contains additional correlated-hopping, pair-hopping and charge–charge interactions of electrons. For even numbers of electrons less than or equal to 2/3-filling, we construct the exact ground states of the model, all of which have the same energy and each of which is the unique ground state for a fixed electron number. It is shown that these ground states are the resonating-valence-bond states which are also regarded as condensed states in which all electrons are in a single two-electron state. We also show that the ground states exhibit off-diagonal long-range order.

arXiv:cond-mat/0309301•Journal of Physics A Mathematical and General•Jan 19, 2004•6 citations

The inseparability of resonating valence bond and on-site pairing long-range orders in doped Hubbard models

Guang-Shan Tian

The concept of the resonating valence bond (RVB) state was originally proposed by Anderson (1987) for the ground state of the positive-U Hubbard model. However, the on-site pairing long-range order is expected to exist in the ground state of the negative-U Hubbard model and to be incompatible with the RVB order. In this article, we shall rigorously prove that, in fact, these two long-range orderings either coexist or are suppressed simultaneously in the global ground states of the doped Hubbard models.

Journal of Physics A Mathematical and General•Oct 21, 1994•3 citations

Numerical simulation of the resonant valence-bond state

J. Callaway

The resonant valence-bond state, proposed by Anderson as a possible ground state in certain antiferromagnetic systems, and relevant to the problem of high-temperature superconductivity, is studied by numerical simulation on a finite cluster. It is found to be the ground state of a simple Hubbard model with a half-filled band on a centered hexagon for a range of intermediate values of the electron interaction parameter. A singlet ground state is obtained away from the half-filled limit for the same parameters.

Physical review. B, Condensed matter•Jun 1, 1987•47 citations

Uniqueness of the ground state in exactly solvable Hubbard, periodic Anderson, and Emery models

Hal Tasaki

We study the exactly solvable strongly interacting electron models recently introduced by Brandt and Giesekus and further generalized by other authors. For a very general class of models, including the Hubbard, the periodic Anderson, and the Emery models with certain hopping matrices and infinitely large on-site Coulomb repulsion on d sites, we prove that the known exact ground state is indeed the unique ground state for a certain electron number. The uniqueness guarantees that one can discuss physics of various strongly interacting electron systems by analyzing the exact ground states.

Physical review. B, Condensed matter•Mar 15, 1994•13 citations

One-dimensional Hubbard model with first- and second-neighbor hopping

T. A. Kaplan

The one-dimensional Hubbard model with first- and second-neighbor hopping, t1 and t2, with t2≊t1/(2)1/2 and large repulsion U, is proposed as a testing ground of Anderson’s idea that the existence of an resonating valence bond ground state in the half-filled-band case will show superconductivity when a finite concentration of holes is introduced. Interestingly, our preliminary calculations in the U=∞ limit for small chains have revealed a new mechanism for enhancement of singlet pairing: We find that for t2<0 the ground state is a singlet, and, for t2<0 and ‖t2/t1‖≪1, the nearest-neighbor extended-singlet-pairing correlation function becomes enhanced appreciably as the temperature decreases below t2.

Journal of Applied Physics•Apr 15, 1988•3 citations

On the bound state of holes for the square-lattice Hubbard model with resonating valence bonds

А. Ф. Барабанов, Leonid A. Maksimov, Andrey V. Mikheyenkov

The Hubbard model for the square planar lattice in the limit t/U<<1 is discussed. The ground state is chosen to be the product of the Hubbard model's exact solutions for four-site blocks. One-particle excitations appear to be Fermi particles with spin 1 / 2 . Their effective mass near the bottom of the band coincides with the effective mass of excitations in the paramagnetic state in the 'Hubbard-I' approximation. However, minima of the spectrum are situated at other points in the Brillouin zone. The possibility of the binding of two excitations into singlet pair with charge 2e is demonstrated. Cohesive energy is calculated to be equal to 0.1t. The superfluid state of the Bose gas of such pairs is assumed to be connected with high-T c superconductivity.

Journal of Physics Condensed Matter•Dec 18, 1989•10 citations
We generalize the exactly solvable Hubbard model with infinitely large on-site Coulomb repulsion recently introduced by Brandt and Giesekus. We point out that the exact ground state can be regarded as a resonating-valence-bond state, and argue that the state may exhibit superconductivity. The existence of a phase with singlet-pair ordering is demonstrated in a simple model on a tree.
We propose a new exactly solvable model of strongly correlated electrons. The model is based on a d – p model of the CuO 2 plane with infinitely large repulsive interactions on Cu-sites, and it contains additional correlated-hopping, pair-hopping and charge–charge interactions of electrons. For even numbers of electrons less than or equal to 2/3-filling, we construct the exact ground states of the model, all of which have the same energy and each of which is the unique ground state for a fixed electron number. It is shown that these ground states are the resonating-valence-bond states which are also regarded as condensed states in which all electrons are in a single two-electron state. We also show that the ground states exhibit off-diagonal long-range order.
The concept of the resonating valence bond (RVB) state was originally proposed by Anderson (1987) for the ground state of the positive-U Hubbard model. However, the on-site pairing long-range order is expected to exist in the ground state of the negative-U Hubbard model and to be incompatible with the RVB order. In this article, we shall rigorously prove that, in fact, these two long-range orderings either coexist or are suppressed simultaneously in the global ground states of the doped Hubbard models.
The resonant valence-bond state, proposed by Anderson as a possible ground state in certain antiferromagnetic systems, and relevant to the problem of high-temperature superconductivity, is studied by numerical simulation on a finite cluster. It is found to be the ground state of a simple Hubbard model with a half-filled band on a centered hexagon for a range of intermediate values of the electron interaction parameter. A singlet ground state is obtained away from the half-filled limit for the same parameters.
We study the exactly solvable strongly interacting electron models recently introduced by Brandt and Giesekus and further generalized by other authors. For a very general class of models, including the Hubbard, the periodic Anderson, and the Emery models with certain hopping matrices and infinitely large on-site Coulomb repulsion on d sites, we prove that the known exact ground state is indeed the unique ground state for a certain electron number. The uniqueness guarantees that one can discuss physics of various strongly interacting electron systems by analyzing the exact ground states.
The one-dimensional Hubbard model with first- and second-neighbor hopping, t1 and t2, with t2≊t1/(2)1/2 and large repulsion U, is proposed as a testing ground of Anderson’s idea that the existence of an resonating valence bond ground state in the half-filled-band case will show superconductivity when a finite concentration of holes is introduced. Interestingly, our preliminary calculations in the U=∞ limit for small chains have revealed a new mechanism for enhancement of singlet pairing: We find that for t2<0 the ground state is a singlet, and, for t2<0 and ‖t2/t1‖≪1, the nearest-neighbor extended-singlet-pairing correlation function becomes enhanced appreciably as the temperature decreases below t2.
The Hubbard model for the square planar lattice in the limit t/U<<1 is discussed. The ground state is chosen to be the product of the Hubbard model's exact solutions for four-site blocks. One-particle excitations appear to be Fermi particles with spin 1 / 2 . Their effective mass near the bottom of the band coincides with the effective mass of excitations in the paramagnetic state in the 'Hubbard-I' approximation. However, minima of the spectrum are situated at other points in the Brillouin zone. The possibility of the binding of two excitations into singlet pair with charge 2e is demonstrated. Cohesive energy is calculated to be equal to 0.1t. The superfluid state of the Bose gas of such pairs is assumed to be connected with high-T c superconductivity.