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

• URL: http://arxiv.org/abs/2205.07235v1
• Date: Sun, 15 May 2022 09:42:18 GMT
• Title: Exact eigenstates of multicomponent Hubbard models: SU($N$) magnetic $\eta$ pairing, weak ergodicity breaking, and partial integrability
• Authors: Masaya Nakagawa, Hosho Katsura, Masahito Ueda
• Abstract summary: Generalized $eta$-pairing mechanism permits construction of eigenstates that feature off-diagonal long-range order and magnetic long-range order. We show that these exact eigenstates constitute integrable subsectors in which the Hubbard Hamiltonian effectively reduces to a non-interacting model.
• Score: 4.511923587827301
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We construct exact eigenstates of multicomponent Hubbard models in arbitrary dimensions by generalizing the $\eta$-pairing mechanism. Our models include the SU($N$) Hubbard model as a special case. Unlike the conventional two-component case, the generalized $\eta$-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 $\eta$ pairs. While the $\eta$-pairing states in the SU(2) Hubbard model are based on the $\eta$-pairing symmetry, the exact eigenstates in the $N$-component system with $N\geq 3$ arise not from symmetry of the Hamiltonian but from a spectrum generating algebra defined in a Hilbert subspace. We exploit this fact to show that the generalized $\eta$-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 $N\geq 3$. Furthermore, we show that these exact eigenstates constitute integrable subsectors in which the Hubbard Hamiltonian effectively reduces to a non-interacting 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 non-thermalization 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.

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