Communications in Theoretical Physics

Exact eigenstates of Hubbard models with and without bond–charge interactions on general graphs

Ming-Yong Ye

Published Jan 19, 2026• 0 citations

Abstract

Abstract We investigate Hubbard models with bond–charge interactions on general graphs. For a Hamiltonian H of such a model, we provide the condition on its parameters under which the η -pairing method can be employed to construct its exact eigenstates. We arrive at this condition by finding that the requirement for the η -pairing state ( η † ) N ∣ 0 〉 to be an eigenstate of H is identical to the requirement for it to be an eigenstate of a Hubbard-type Hamiltonian H m without bond–charge interactions. When the condition for ( η † ) N ∣ 0 〉 to be an eigenstate of the Hubbard-type Hamiltonian H m is satisfied, we demonstrate that there are additional states, distinct from ( η † ) N ∣ 0 〉 , which are also exact eigenstates of H m . Our results enhance the understanding of Hubbard models on general graphs, both with and without bond–charge interactions.

DOI: 10.1088/1572-9494/ae2ded

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Communications in Theoretical Physics

Exact eigenstates of Hubbard models with and without bond–charge interactions on general graphs

Ming-Yong Ye

Published Jan 19, 2026• 0 citations

Publisher

Abstract

DOI: 10.1088/1572-9494/ae2ded

Related papers

Eta-pairing states in Hubbard models with bond-charge interactions on general graphs

Ming-Yong Ye

We investigate Hubbard models with bond-charge interactions on general graphs. For a Hamiltonian $H$ of such a model, we provide the condition on its parameters under which the $η$ -pairing method can be employed to construct its exact eigenstates. We arrive at this condition by finding that the requirement for the $η$ -pairing state $(η^\dagger)^N |0\rangle$ to be an eigenstate of $H$ is identical to the requirement for it to be an eigenstate of a Hubbard-type Hamiltonian $H_m$ . When the condition for $(η^\dagger)^N |0\rangle$ to be an eigenstate of the Hubbard-type Hamiltonian $H_m$ is satisfied, we demonstrate that there are additional states, distinct from $(η^\dagger)^N |0\rangle$ , which are also exact eigenstates of $H_m$ . Our results enhance the understanding of Hubbard models on general graphs, both with and without bond-charge interactions.We investigate Hubbard models with bond-charge interactions on general graphs. For a Hamiltonian $H$ of such a model, we provide the condition on its parameters under which the $η$-pairing method can be employed to construct its exact eigenstates. We arrive at this condition by finding that the requirement for the $η$-pairing state $(η^\dagger)^N |0\rangle$ to be an eigenstate of $H$ is identical to the requirement for it to be an eigenstate of a Hubbard-type Hamiltonian $H_m$. When the condition for $(η^\dagger)^N |0\rangle$ to be an eigenstate of the Hubbard-type Hamiltonian $H_m$ is satisfied, we demonstrate that there are additional states, distinct from $(η^\dagger)^N |0\rangle$, which are also exact eigenstates of $H_m$. Our results enhance the understanding of Hubbard models on general graphs, both with and without bond-charge interactions.

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Daniel K. Mark, Olexei I. Motrunich

The $\ensuremath{\eta}$-pairing states are a set of exactly known eigenstates of the Hubbard model on hypercubic lattices, first discovered by Yang [C. N. Yang, Phys. Rev. Lett. 63, 2144 (1989)]. These states are not many-body scar states in the Hubbard model because they occupy unique symmetry sectors defined by the so-called $\ensuremath{\eta}$-pairing SU(2) symmetry. We study an extended Hubbard model with bond-charge interactions, popularized by Hirsch [J. E. Hirsch, Physica C 158, 326 (1989)], where the $\ensuremath{\eta}$-pairing states survive without the $\ensuremath{\eta}$-pairing symmetry and become true scar states. We also discuss similarities between the $\ensuremath{\eta}$-pairing states and exact scar towers in the spin-1 XY model found by Schecter and Iadecola [M. Schecter and T. Iadecola, Phys. Rev. Lett. 123, 147201 (2019)], and systematically arrive at all nearest-neighbor terms that preserve such scar towers in one dimension. We also generalize these terms to arbitrary bipartite lattices. Our study of the spin-1 XY model also leads us to several scarred models, including a spin-1/2 ${J}_{1}\ensuremath{-}{J}_{2}$ model with Dzyaloshinskii-Moriya interaction, in realistic quantum magnet settings in one and two dimensions.The $\ensuremath{\eta}$-pairing states are a set of exactly known eigenstates of the Hubbard model on hypercubic lattices, first discovered by Yang [C. N. Yang, Phys. Rev. Lett. 63, 2144 (1989)]. These states are not many-body scar states in the Hubbard model because they occupy unique symmetry sectors defined by the so-called $\ensuremath{\eta}$-pairing SU(2) symmetry. We study an extended Hubbard model with bond-charge interactions, popularized by Hirsch [J. E. Hirsch, Physica C 158, 326 (1989)], where the $\ensuremath{\eta}$-pairing states survive without the $\ensuremath{\eta}$-pairing symmetry and become true scar states. We also discuss similarities between the $\ensuremath{\eta}$-pairing states and exact scar towers in the spin-1 XY model found by Schecter and Iadecola [M. Schecter and T. Iadecola, Phys. Rev. Lett. 123, 147201 (2019)], and systematically arrive at all nearest-neighbor terms that preserve such scar towers in one dimension. We also generalize these terms to arbitrary bipartite lattices. Our study of the spin-1 XY model also leads us to several scarred models, including a spin-1/2 ${J}_{1}\ensuremath{-}{J}_{2}$ model with Dzyaloshinskii-Moriya interaction, in realistic quantum magnet settings in one and two dimensions.

arXiv:2004.13800Physical review. B./Physical review. BAug 24, 2020133 citations

We investigate Hubbard models with bond-charge interactions on general graphs. For a Hamiltonian

H

of such a model, we provide the condition on its parameters under which the

η

-pairing method can be employed to construct its exact eigenstates. We arrive at this condition by finding that the requirement for the

η

-pairing state

(η^\dagger)^N |0\rangle

to be an eigenstate of

H

is identical to the requirement for it to be an eigenstate of a Hubbard-type Hamiltonian

H_m

. When the condition for

(η^\dagger)^N |0\rangle

to be an eigenstate of the Hubbard-type Hamiltonian

H_m

is satisfied, we demonstrate that there are additional states, distinct from

(η^\dagger)^N |0\rangle

, which are also exact eigenstates of

H_m

. Our results enhance the understanding of Hubbard models on general graphs, both with and without bond-charge interactions.

U

. In this work, we present a generalized Hubbard model containing a variety of pseudospin terms that break the

{\mathrm{SO}}_{4}

symmetry but retain the $\ensuremath{\eta}$-pairing symmetry. This allows us to construct a variety of correlated systems possessing $\ensuremath{\eta}$-pairing eigenstates. We exemplify our findings by considering a modified Hubbard model associated with alternative magnetic fields and on-site repulsion. We find that the same quasi-$\ensuremath{\eta}$-pairing eigenstate exhibits two distinct dynamic behaviors in the two models. Numerical results of the time evolution driven by several typical Hamiltonians accord with the analytic predictions and provide a method for the control of an $\ensuremath{\eta}$-pairing wave packet with the aid of a time-dependent Hamiltonian.

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.