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

• URL: http://arxiv.org/abs/2012.13415v1
• Date: Thu, 24 Dec 2020 19:00:11 GMT
• Title: Simulating non-Hermitian dynamics of a multi-spin quantum system and an emergent central spin model
• Authors: Anant V. Varma and Sourin Das
• Abstract summary: It is possible to simulate the dynamics of a single spin-$1/2$ ($mathsfPT$ symmetric) system by embedding it into a subspace of a larger Hilbert space with unitary dynamics. We visualize it as a strongly correlated central spin model with the additional spin-$1/2$ playing the role of central spin.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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