Simulating non-Hermitian dynamics of a multi-spin quantum system and an emergent central spin model

It is possible to simulate the dynamics of a single spin-1/2 $mathsf{PT }$ symmetric system by conveniently embedding it into a subspace of a larger Hilbert space with unitary dynamics. Our goal is to formulate a many body generalization of this idea i.e., embedding many body non-Hermitian dynamics. As a first step in this direction, we investigate embedding of "N" non-interacting spin-1/2 $mathsf{PT }$ symmetric degrees of freedom, thereby unfolding the complex nature of such an embedding procedure. It turns out that the resulting Hermitian Hamiltonian represents a cluster of N+1 spin halves with "all to all", q-body interaction terms $q=1,...,N+1$ in which the additional spin-1/2 is a part of the larger embedding space. We can visualize it as a strongly correlated central spin model with the additional spin-1/2 playing the role of central spin. We find that due to the orthogonality catastrophe, even a vanishing small exchange field applied along the anisotropy axis of the central spin leads to a strong suppression of its decoherence arising from spin-flipping perturbations.