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:2109.07010 · Physical review. B./Physical review. B

Exact eigenstates of extended SU ( N ) Hubbard models: Generalization of η -pairing states with N -particle off-diagonal long-range order

Hironobu Yoshida, Hosho Katsura

Published Jan 25, 2022• 19 citations
arXivHTMLPDF

Abstract

We consider $N$-particle generalizations of $\ensuremath{\eta}$-pairing states in a chain of $N$-component fermions and show that these states are exact (high-energy) eigenstates of an extended $\mathrm{SU}(N)$ Hubbard model. We compute the singlet correlation function of the states and find that its behavior is qualitatively different for even and odd $N$. When $N$ is even, these states exhibit off-diagonal long-range order in $N$-particle reduced density matrix. On the other hand, when $N$ is odd, the correlations decay exponentially with distance in the bulk, but end-to-end correlations do not vanish in the thermodynamic limit. Finally, we prove that these states are the unique ground states of suitably tailored Hamiltonians.

DOI
10.1103/physrevb.105.024520

Related papers

Exact eigenstates of multicomponent Hubbard models: SU( N ) magnetic η pairing, weak ergodicity breaking, and partial integrability

Masaya Nakagawa, Hosho Katsura, Masahito Ueda

We construct exact eigenstates of multicomponent Hubbard models in arbitrary dimensions by generalizing the η -pairing mechanism. Our models include the SU ( N ) Hubbard model as a special case. Unlike the conventional two-component case, the generalized η -pairing mechanism permits the construction of eigenstates that feature off-diagonal long-range order and magnetic long-range order. These states form fragmented fermionic condensates due to a simultaneous condensation of multicomponent η pairs. While the η -pairing states in the SU(2) Hubbard model are based on the η -pairing symmetry, the exact eigenstates in the N -component system with N ≥ 3 arise not from symmetry of the Hamiltonian but from a spectrum generating algebra defined in a restricted Hilbert space. We exploit this fact to show that the generalized η -pairing eigenstates do not satisfy the eigenstate thermalization hypothesis and serve as quantum many-body scar states. This result indicates a weak breakdown of ergodicity in the N -component Hubbard models for N ≥ 3 . Furthermore, we show that these exact eigenstates constitute integrable subsectors in which the Hubbard Hamiltonian effectively reduces to a noninteracting model. This partial integrability causes various multicomponent Hubbard models to weakly break ergodicity. We propose a method of harnessing dissipation to distill the integrable part of the dynamics and elucidate a mechanism of nonthermalization caused by dissipation. This work establishes the coexistence of off-diagonal long-range order and SU ( N ) magnetism in excited eigenstates of the multicomponent Hubbard models, which presents a possibility of novel out-of-equilibrium pairing states of multicomponent fermions. These models unveil a unique feature of quantum thermalization of multicomponent fermions, which can experimentally be tested with cold-atom quantum simulators. Published by the American Physical Society 2024

arXiv:2205.07235•Physical Review Research•Dec 11, 2024•17 citations

η pairing and off-diagonal long-range order in a Hubbard model

Chen Ning Yang

It is shown in a simple Hubbard model that through a mechanism called \ensuremath{\eta} pairing one can construct many eigenstates of the Hamiltonian possessing off-diagonal long-range order. The intrapair distance is small. It is shown that these eigenstates are metastable and possess an energy gap.

Physical Review Letters•Nov 6, 1989•603 citations

New exactly solvable model of strongly correlated electrons motivated by high- T c superconductivity

Fabian H. L. Eßler, V. E. Korepin, Kareljan Schoutens

We present a new model describing strongly correlated electrons on a general d-dimensional lattice. It is an extended Hubbard model and it contains the t-J model as a special case. The model naturally describes local electron pairs, which can move coherently at arbitrary momentum. By using an \ensuremath{\eta}-pairing mechanism we can construct eigenstates of the Hamiltonian with off-diagonal long-range order. In the attractive case the exact ground state is superconducting in any number of dimensions. On a one-dimensional lattice, the model is exactly solvable by Bethe ansatz.

arXiv:cond-mat/9209002•Physical Review Letters•May 11, 1992•265 citations

Coherent pairing states for the Hubbard model

A. I. Solomon, K. A. Penson

We consider the Hubbard model and its extensions on bipartite lattices. We define a dynamical group based on the -pairing operators introduced by Yang, and define coherent pairing states, which are combinations of eigenfunctions of -operators. These states permit exact calculations of numerous physical properties of the system, including energy, various fluctuations and correlation functions, including pairing off-diagonal long-range order to all orders. This approach is complementary to BCS, in that these are superconducting coherent states associated with the exact model, although they are not eigenstates of the Hamiltonian.

arXiv:cond-mat/9712228•Journal of Physics A Mathematical and General•May 8, 1998•6 citations

η -pairing ground states in the non-Hermitian Hubbard model

X. Z. Zhang, Z. Song

The introduction of non-Hermiticity has greatly enriched the research field of traditional condensed matter physics and eventually led to a series of discoveries of exotic phenomena. We investigate the effect of non-Hermitian imaginary hoppings on the Hubbard model. The exact bound-pair solution shows that the electron-electron correlation suppresses the non-Hermiticity, resulting in off-diagonal long-range order (ODLRO) ground state in the attractive Hubbard model. In a large $U$ limit, such non-Hermiticity contributes an extra minus sign in the virtual exchange of the particles. As a consequence, the energy of the effective spin model describing the behavior of the ground state and low energy excitations will be reversed. The corresponding ground state experiences a transition from antiferromagnetism to ferromagnetism characterized by the appearance of a non-decaying correlation function. The numerical result indicates that the $\ensuremath{\eta}$-pairing ground state exits in 1D and 2D systems and is insensitive to the disorder. We further propose a protocol to adiabatically generate the $\ensuremath{\eta}$-pairing state. Our results provide a promising approach for the non-Hermitian strongly correlated system.

arXiv:2012.15577•Physical review. B./Physical review. B•Jun 23, 2021•23 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
We consider NNN-particle generalizations of \ensuremathη\ensuremath{\eta}\ensuremathη-pairing states in a chain of NNN-component fermions and show that these states are exact (high-energy) eigenstates of an extended SU(N)\mathrm{SU}(N)SU(N) Hubbard model. We compute the singlet correlation function of the states and find that its behavior is qualitatively different for even and odd NNN. When NNN is even, these states exhibit off-diagonal long-range order in NNN-particle reduced density matrix. On the other hand, when NNN is odd, the correlations decay exponentially with distance in the bulk, but end-to-end correlations do not vanish in the thermodynamic limit. Finally, we prove that these states are the unique ground states of suitably tailored Hamiltonians.
We construct exact eigenstates of multicomponent Hubbard models in arbitrary dimensions by generalizing the η -pairing mechanism. Our models include the SU ( N ) Hubbard model as a special case. Unlike the conventional two-component case, the generalized η -pairing mechanism permits the construction of eigenstates that feature off-diagonal long-range order and magnetic long-range order. These states form fragmented fermionic condensates due to a simultaneous condensation of multicomponent η pairs. While the η -pairing states in the SU(2) Hubbard model are based on the η -pairing symmetry, the exact eigenstates in the N -component system with N ≥ 3 arise not from symmetry of the Hamiltonian but from a spectrum generating algebra defined in a restricted Hilbert space. We exploit this fact to show that the generalized η -pairing eigenstates do not satisfy the eigenstate thermalization hypothesis and serve as quantum many-body scar states. This result indicates a weak breakdown of ergodicity in the N -component Hubbard models for N ≥ 3 . Furthermore, we show that these exact eigenstates constitute integrable subsectors in which the Hubbard Hamiltonian effectively reduces to a noninteracting model. This partial integrability causes various multicomponent Hubbard models to weakly break ergodicity. We propose a method of harnessing dissipation to distill the integrable part of the dynamics and elucidate a mechanism of nonthermalization caused by dissipation. This work establishes the coexistence of off-diagonal long-range order and SU ( N ) magnetism in excited eigenstates of the multicomponent Hubbard models, which presents a possibility of novel out-of-equilibrium pairing states of multicomponent fermions. These models unveil a unique feature of quantum thermalization of multicomponent fermions, which can experimentally be tested with cold-atom quantum simulators. Published by the American Physical Society 2024
We present a new model describing strongly correlated electrons on a general d-dimensional lattice. It is an extended Hubbard model and it contains the t-J model as a special case. The model naturally describes local electron pairs, which can move coherently at arbitrary momentum. By using an \ensuremath{\eta}-pairing mechanism we can construct eigenstates of the Hamiltonian with off-diagonal long-range order. In the attractive case the exact ground state is superconducting in any number of dimensions. On a one-dimensional lattice, the model is exactly solvable by Bethe ansatz.
We consider the Hubbard model and its extensions on bipartite lattices. We define a dynamical group based on the -pairing operators introduced by Yang, and define coherent pairing states, which are combinations of eigenfunctions of -operators. These states permit exact calculations of numerous physical properties of the system, including energy, various fluctuations and correlation functions, including pairing off-diagonal long-range order to all orders. This approach is complementary to BCS, in that these are superconducting coherent states associated with the exact model, although they are not eigenstates of the Hamiltonian.
The introduction of non-Hermiticity has greatly enriched the research field of traditional condensed matter physics and eventually led to a series of discoveries of exotic phenomena. We investigate the effect of non-Hermitian imaginary hoppings on the Hubbard model. The exact bound-pair solution shows that the electron-electron correlation suppresses the non-Hermiticity, resulting in off-diagonal long-range order (ODLRO) ground state in the attractive Hubbard model. In a large UUU limit, such non-Hermiticity contributes an extra minus sign in the virtual exchange of the particles. As a consequence, the energy of the effective spin model describing the behavior of the ground state and low energy excitations will be reversed. The corresponding ground state experiences a transition from antiferromagnetism to ferromagnetism characterized by the appearance of a non-decaying correlation function. The numerical result indicates that the $\ensuremath{\eta}$-pairing ground state exits in 1D and 2D systems and is insensitive to the disorder. We further propose a protocol to adiabatically generate the $\ensuremath{\eta}$-pairing state. Our results provide a promising approach for the non-Hermitian strongly correlated system.