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

Abstract

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 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 longrange 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.

Quantum many-body scars of spinless fermions with density-assisted hopping in higher dimensions

“…For a deeper understanding of the mechanism of QMBS, it is helpful to have a variety of models with exact QMBS in higher dimensions; therefore, new examples of such models are desired. Furthermore, the majority of the studies deal with spin systems, whereas there are fewer examples of QMBS in particle systems such as fermionic systems [39][40][41][42][43][44][45][46].…”

Condensation of Cooper triples

“…Moreover, multi-component Fermi gases can be realized by using different hyperfine states of ultracold atoms (e.g., 6 Li [10], 173 Yb [11]). The long-range order in a multi-component attractive Hubbard model has also been discussed theoretically [12,13]. The realization of a three-body interaction, which is deeply related to the formation of Cooper triples, has also been proposed in cold atomic systems [3,7,14,15].…”

Spin, Charge, and η -Spin Separation in One-Dimensional Photodoped Mott Insulators

“…This effective Hamiltonian explicitly conserves the number of doublons and holons. Up to Oðt 2 hop =UÞ, it takes the form [51][52][53]. ĤU;shift describes the shift of the local interaction and Ĥ3−site represents three-site terms such as correlated doublon hoppings, see Supplemental Material [50].…”