Exact eigenstates of multicomponent Hubbard models: SU($N$) magnetic $η$ pairing, weak ergodicity breaking, and partial integrability
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2022
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910743573561344 |
|---|---|
| author | Nakagawa, Masaya Katsura, Hosho Ueda, Masahito |
| author_facet | Nakagawa, Masaya Katsura, Hosho Ueda, Masahito |
| contents | 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 $N\geq 3$ 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 $η$-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 $N\geq 3$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_07235 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Exact eigenstates of multicomponent Hubbard models: SU($N$) magnetic $η$ pairing, weak ergodicity breaking, and partial integrability Nakagawa, Masaya Katsura, Hosho Ueda, Masahito Strongly Correlated Electrons Quantum Gases Statistical Mechanics Superconductivity Quantum Physics 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 $N\geq 3$ 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 $η$-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 $N\geq 3$. 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. |
| title | Exact eigenstates of multicomponent Hubbard models: SU($N$) magnetic $η$ pairing, weak ergodicity breaking, and partial integrability |
| topic | Strongly Correlated Electrons Quantum Gases Statistical Mechanics Superconductivity Quantum Physics |
| url | https://arxiv.org/abs/2205.07235 |