Simulation of non-Hermitian dynamics of many-body quantum systems

We investigate the complexity of simulating many-body non-Hermitian dynamics using the embedding method, as non-Hermitian systems do not exist in nature as closed systems. We show that simulation of even simplest many-body non-Hermitian system namely a system of N-free spin-1/2s or fermions would require a strongly correlated Hermitian system in higher dimensions, with a minimal dilation of Hilbert space. We further show that such highly interacting Hermitian system can be visualized as a central spin or fermion model and exhibit many-body features like orthogonality catastrophe.