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

arXiv:cond-mat/0310615 · Journal of the Physical Society of Japan

Exact Electron-Pairing Ground States of Tight-Binding Models with Local Attractive Interactions

Akinori Tanaka

Published May 15, 2004• 2 citations
arXivHTMLPDF

Abstract

We present a class of exactly solvable models of correlated electrons. The models are defined in any dimension $d$ and consist of electron-hopping terms and local attractive interactions between electrons. For each even number of electrons less than or equal to $1/(d+1)$-filling, we find the exact ground state in which all electrons form pairs of a certain type, and thus the models exhibit an electron-pair condensation.

DOI
10.1143/jpsj.73.1107

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

Exactly Solvable Model of Correlated Lattice Electrons in Any Dimensions

Yasuhiro Hatsugai, Mahito Kohmoto

We present an exactly solvable Hamiltonian which consists of nearest neighbor hopping and long-range interaction. The ground state and the thermodynamic quantities are analytically obtained in any dimensions. In a repulsive case, the Luttinger's theorem breaks down and the hypothesis of the adiabatic continuation no longer holds. At half filling, we show the existence of a metal-insulator transition as a function of the strength of the interaction. The zero energy excitation disappears at the critical value of the interaction when we increase the interaction. In this case, the system is an insulator. The charge compressibility behaves as κ≈|1-ρ| 1-2/ d near half filling in d dimensions where ρ is the density of electrons. At other fillings, there is always a zero energy excitation and the system is metallic. When the interaction is attractive, the ground state is composed of pairs of electrons with opposite spins. The low energy excitations, however, is not a particle-hole type of a non-interacting case but a pairwise excitation across the Fermi surface.

Journal of the Physical Society of Japan•Jun 1, 1992•99 citations

Rigorous results on superconducting ground states for attractive extended Hubbard models

Arianna Montorsi, David K Campbell

We show that the exact ground state for a class of extended Hubbard models including bond-charge, exchange, and pair-hopping terms, is the Yang ``\ensuremath{\eta}-paired'' state for any nonvanishing positive value of the pair-hopping amplitude, at least when the on-site Coulomb interaction is attractive enough and the remaining physical parameters satisfy a single constraint. The ground state is thus rigorously superconducting. Our result holds on a bipartite lattice in any dimension, at any band filling, and for arbitrary electron hopping. \textcopyright{} 1996 The American Physical Society.

arXiv:cond-mat/9502027•Physical review. B, Condensed matter•Mar 1, 1996•36 citations

Extended Hubbard model with unconventional pairing in two dimensions

Akinori Tanaka, Masanori Yamanaka

We rigorously prove that an extended Hubbard model with attraction in two dimensions has an unconventional pairing ground state for any electron filling. The anisotropic spin-0 or anisotropic spin-1 pairing symmetry is realized, depending on a phase parameter characterizing the type of local attractive interactions. In both cases the ground state is unique. It is also shown that in a special case, where there are no electron-hopping terms, the ground state has Ising-type N\'eel order at half-filling, when on-site repulsion is furthermore added. Physical applications are mentioned.

arXiv:cond-mat/0405548•Physical Review B•Jun 2, 2005•1 citation

Model of Fermions with Correlated Hopping (Integrable Cases)

Igor N. Karnaukhov

We present a new model describing strongly correlated electrons on a lattice. The model naturally describes the nearest-neighbor hopping of electrons and local electron pairs and the interaction between them. It is an extended Hubbard model exactly solvable in one dimension for some special values of the coupling constants. The Bethe ansatz equation are obtained and a ground state is discussed.

Physical Review Letters•Aug 22, 1994•61 citations

Rigorous Results on Unconventional Pairings in Two Dimensions

Akinori Tanaka, Masanori Yamanaka

We rigorously prove that an extended Hubbard model with attraction in two dimensions has an unconventional pairing ground state for any electron filling. The anisotropic spin-0 or anisotropic spin-1 pairing symmetry is realized, depending on a phase parameter characterizing the type of local attractive interactions. In both cases the ground state is unique. It is also shown that in a special case, where there are no electron hopping terms, the ground state has Ising-type Neel order at half-filling, when on-site repulsion is furthermore added. Physical applications are mentioned.

•May 24, 2004•0 citations
We present a class of exactly solvable models of correlated electrons. The models are defined in any dimension ddd and consist of electron-hopping terms and local attractive interactions between electrons. For each even number of electrons less than or equal to 1/(d+1)1/(d+1)1/(d+1)-filling, we find the exact ground state in which all electrons form pairs of a certain type, and thus the models exhibit an electron-pair condensation.
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.
We present an exactly solvable Hamiltonian which consists of nearest neighbor hopping and long-range interaction. The ground state and the thermodynamic quantities are analytically obtained in any dimensions. In a repulsive case, the Luttinger's theorem breaks down and the hypothesis of the adiabatic continuation no longer holds. At half filling, we show the existence of a metal-insulator transition as a function of the strength of the interaction. The zero energy excitation disappears at the critical value of the interaction when we increase the interaction. In this case, the system is an insulator. The charge compressibility behaves as κ≈|1-ρ| 1-2/ d near half filling in d dimensions where ρ is the density of electrons. At other fillings, there is always a zero energy excitation and the system is metallic. When the interaction is attractive, the ground state is composed of pairs of electrons with opposite spins. The low energy excitations, however, is not a particle-hole type of a non-interacting case but a pairwise excitation across the Fermi surface.
We show that the exact ground state for a class of extended Hubbard models including bond-charge, exchange, and pair-hopping terms, is the Yang ``\ensuremath{\eta}-paired'' state for any nonvanishing positive value of the pair-hopping amplitude, at least when the on-site Coulomb interaction is attractive enough and the remaining physical parameters satisfy a single constraint. The ground state is thus rigorously superconducting. Our result holds on a bipartite lattice in any dimension, at any band filling, and for arbitrary electron hopping. \textcopyright{} 1996 The American Physical Society.
We rigorously prove that an extended Hubbard model with attraction in two dimensions has an unconventional pairing ground state for any electron filling. The anisotropic spin-0 or anisotropic spin-1 pairing symmetry is realized, depending on a phase parameter characterizing the type of local attractive interactions. In both cases the ground state is unique. It is also shown that in a special case, where there are no electron-hopping terms, the ground state has Ising-type N\'eel order at half-filling, when on-site repulsion is furthermore added. Physical applications are mentioned.
We rigorously prove that an extended Hubbard model with attraction in two dimensions has an unconventional pairing ground state for any electron filling. The anisotropic spin-0 or anisotropic spin-1 pairing symmetry is realized, depending on a phase parameter characterizing the type of local attractive interactions. In both cases the ground state is unique. It is also shown that in a special case, where there are no electron hopping terms, the ground state has Ising-type Neel order at half-filling, when on-site repulsion is furthermore added. Physical applications are mentioned.