Simulating many-body non-Hermitian PT-symmetric spin dynamics

It is possible to simulate the dynamics of a single spin-1/2 (PT-symmetric) system by conveniently embedding it into a subspace of a larger Hilbert space, undergoing unitary dynamics governed by a Hermitian Hamiltonian. Our goal is to analyze a many-body generalization of this idea, i.e., embedding many-body nonHermitian dynamics. As a first step in this direction, we investigate embedding of N noninteracting spin-1/2 (PT-symmetric) degrees of freedom, thereby unfolding the complex nature of the embedding Hamiltonian. It turns out that the resulting Hermitian Hamiltonian of N + 1 spin halves comprises all to all, q-body interaction terms (q = 1, . . . , N + 1) where the additional spin-1/2 is a part of the larger embedding space. We show that the presence of finite entanglement in the eigenstates of the resulting cluster of N + 1 spin halves ensures the nonvanishing probability of post-selection of the additional spin-1/2, which is essential for the embedding to be practicable. Finally, we also note that our study can be identified with a central spin model where orthogonality catastrophe owing to the finite entanglement plays a central role in protecting the additional spin-1/2 degree of freedom from decoherence. It is possible to simulate the dynamics of a single spin-1/2 (PT-symmetric) system by conveniently embedding it into a subspace of a larger Hilbert space, undergoing unitary dynamics governed by a Hermitian Hamiltonian. Our goal is to analyze a many-body generalization of this idea, i.e., embedding many-body nonHermitian dynamics. As a first step in this direction, we investigate embedding of N noninteracting spin-1/2 (PT-symmetric) degrees of freedom, thereby unfolding the complex nature of the embedding Hamiltonian. It turns out that the resulting Hermitian Hamiltonian of N + 1 spin halves comprises all to all, q-body interaction terms (q = 1, . . . , N + 1) where the additional spin-1/2 is a part of the larger embedding space. We show that the presence of finite entanglement in the eigenstates of the resulting cluster of N + 1 spin halves ensures the nonvanishing probability of post-selection of the additional spin-1/2, which is essential for the embedding to be practicable. Finally, we also note that our study can be identified with a central spin model where orthogonality catastrophe owing to the finite entanglement plays a central role in protecting the additional spin-1/2 degree of freedom from decoherence.

Automated summary

By embedding N noninteracting spin-1/2 (PT-symmetric) degrees of freedom, it was demonstrated that the resulting Hermitian Hamiltonian of N + 1 spin halves includes all to all, q-body interaction terms. With finite entanglement in the eigenstates of the resulting cluster, the probability of post-selection of the additional spin-1/2 remains nonvanishing, crucial for practical embedding. This study's connection to a central spin model highlights the role of orthogonality catastrophe in protecting the additional spin-1/2 degree of freedom from decoherence.