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We construct exact eigenstates of multicomponent Hubbard models in arbitrarydimensions by generalizing the $\eta$-pairing mechanism. Our models include theSU($N$) Hubbard model as a special case. Unlike the conventional two-componentcase, the generalized $\eta$-pairing mechanism permits the construction ofeigenstates that feature off-diagonal long-range order and magnetic long-rangeorder. These states form fragmented fermionic condensates due to a simultaneouscondensation of multicomponent $\eta$ pairs. While the $\eta$-pairing states inthe SU(2) Hubbard model are based on the $\eta$-pairing symmetry, the exacteigenstates in the $N$-component system with $N\geq 3$ arise not from symmetryof the Hamiltonian but from a spectrum generating algebra defined in a Hilbertsubspace. We exploit this fact to show that the generalized $\eta$-pairingeigenstates do not satisfy the eigenstate thermalization hypothesis and serveas quantum many-body scar states. This result indicates a weak breakdown ofergodicity in the $N$-component Hubbard models for $N\geq 3$. Furthermore, weshow that these exact eigenstates constitute integrable subsectors in which theHubbard Hamiltonian effectively reduces to a non-interacting model. Thispartial integrability causes various multicomponent Hubbard models to weaklybreak ergodicity. We propose a method of harnessing dissipation to distill theintegrable part of the dynamics and elucidate a mechanism of non-thermalizationcaused by dissipation. This work establishes the coexistence of off-diagonallong-range order and SU($N$) magnetism in excited eigenstates of themulticomponent Hubbard models, which presents a possibility of novelout-of-equilibrium pairing states of multicomponent fermions. These modelsunveil a unique feature of quantum thermalization of multicomponent fermions,which can experimentally be tested with cold-atom quantum simulators.

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