论文标题
多组分哈伯德模型的确切本质：su（$ n $）磁性$η$配对，弱牙性破坏和部分整合性
Exact eigenstates of multicomponent Hubbard models: SU($N$) magnetic $η$ pairing, weak ergodicity breaking, and partial integrability
论文作者
论文摘要
我们通过概括$η$ pairing机制来构建任意维度的多组分哈伯德模型的精确本征态。我们的模型包括SU（$ n $）Hubbard模型作为特殊情况。与常规的两组式案例不同，广义$η$ pairing机制允许构建特征状态，这些特征状态具有偏高的长距离顺序和磁性远距离顺序。由于多组分$η$ pairs的同时凝结，这些状态形成了碎片的费米冷凝水。 SU（2）Hubbard模型中的$η$ pairing状态是基于$η$ pairing的对称性，而具有$ n $ n \ geq 3 $的$ n $ component System中的确切特征是不是来自汉密尔顿的对称性，而是来自applesprum Generation Algebra a a algebra a a algebra subspep subspep subspace。我们利用这一事实表明，广义的$η$ pairing特征状态不满足特征态热假说，并用作量子多体疤痕状态。该结果表明，在$ n \ geq 3 $的$ n $组成哈伯德模型中，细分差异很弱。此外，我们表明这些精确的本征构成了可集成的子行业，其中哈伯族哈密顿式的汉密尔顿人有效地减少了非相互作用模型。这种部分的集成性导致各种多组分哈伯德模型薄弱地破坏了牙齿。我们提出了一种利用耗散的方法来提炼动力学的可集成部分，并阐明耗散引起的非热化机制。这项工作确立了在多组分哈伯德模型的激发特征状态下，非对角线长距离顺序和su（$ n $）磁性的共存，该模型具有新型多组分费米子的新型外部配对状态的可能性。这些模型推出了多组分费物的量子热化的独特特征，可以通过冷原子量子模拟器对其进行实验测试。
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.
