Statistical aspects of a quantum Hopfield model

In this paper, we study the eigenstate properties of a quantum Hopfield model by the exact diagonalization method. The local permutational symmetry in this model organizes the spins into clusters, which can each be considered a large quantum spin interacting with others. It is shown that such a quantum Hopfield model, even though without dissipation, is interesting in its own right as an example of quantum frustrated magnetism and quantum spin glass. It exhibits three distinct phases: a low-energy spin-glass phase at a low transverse field, a thermal paramagnetic phase at a high transverse field, and a nonthermal high-energy paramagnetic phase. The dynamics of the revival probability starting from a memory pattern in such a closed quantum many-body model has also been studied.