Exact eigenstates of multicomponent Hubbard models: SU(N) magnetic η pairing, weak ergodicity breaking, and partial integrability
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 e...
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American Physical Society
2024-12-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.6.043259 |
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| author | Masaya Nakagawa Hosho Katsura Masahito Ueda |
| author_facet | Masaya Nakagawa Hosho Katsura Masahito Ueda |
| author_sort | Masaya Nakagawa |
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| description | 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. |
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| issn | 2643-1564 |
| language | English |
| publishDate | 2024-12-01 |
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| spelling | doaj-art-6e62b20aa4174ac6b2702cc13b3e293c2025-08-20T02:33:47ZengAmerican Physical SocietyPhysical Review Research2643-15642024-12-016404325910.1103/PhysRevResearch.6.043259Exact eigenstates of multicomponent Hubbard models: SU(N) magnetic η pairing, weak ergodicity breaking, and partial integrabilityMasaya NakagawaHosho KatsuraMasahito UedaWe 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.http://doi.org/10.1103/PhysRevResearch.6.043259 |
| spellingShingle | Masaya Nakagawa Hosho Katsura Masahito Ueda Exact eigenstates of multicomponent Hubbard models: SU(N) magnetic η pairing, weak ergodicity breaking, and partial integrability Physical Review Research |
| title | Exact eigenstates of multicomponent Hubbard models: SU(N) magnetic η pairing, weak ergodicity breaking, and partial integrability |
| title_full | Exact eigenstates of multicomponent Hubbard models: SU(N) magnetic η pairing, weak ergodicity breaking, and partial integrability |
| title_fullStr | Exact eigenstates of multicomponent Hubbard models: SU(N) magnetic η pairing, weak ergodicity breaking, and partial integrability |
| title_full_unstemmed | Exact eigenstates of multicomponent Hubbard models: SU(N) magnetic η pairing, weak ergodicity breaking, and partial integrability |
| title_short | Exact eigenstates of multicomponent Hubbard models: SU(N) magnetic η pairing, weak ergodicity breaking, and partial integrability |
| title_sort | exact eigenstates of multicomponent hubbard models su n magnetic η pairing weak ergodicity breaking and partial integrability |
| url | http://doi.org/10.1103/PhysRevResearch.6.043259 |
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