Typically, it is assumed that a high-energy eigenstate of a generic interacting quantum many-body Hamiltonian is thermal and obeys the eigenstate thermalization hypothesis. In this work, we show that the paramagnetic phase of a quantum Hopfield neural network model is delocalized but nonergodic. The combination of permutational symmetry and frustration in this model organize its high-energy eigenstates into clusters, which can each be considered a large quantum spin and has no correlation with others. This model provides another ergodicity-breaking mechanism in quantum many-body systems.

中文翻译：

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量子神经网络中的非遍历离域顺磁态

通常，假设通用相互作用的量子多体哈密顿量的高能本征态是热的并且服从本征态热化假设。在这项工作中，我们证明了量子 Hopfield 神经网络模型的顺磁相是离域的，但非遍历的。该模型中置换对称和挫折的结合将其高能本征态组织成簇，每个都可以被认为是一个大的量子自旋，并且与其他的没有相关性。该模型在量子多体系统中提供了另一种遍历性破坏机制。