Covariance-based method for eigenstate factorization and generalized singlets

• URL: http://arxiv.org/abs/2311.04426v2
• Date: Mon, 18 Nov 2024 21:04:08 GMT
• Title: Covariance-based method for eigenstate factorization and generalized singlets
• Authors: Federico Petrovich, R. Rossignoli, N. Canosa,
• Abstract summary: We derive a general method for determining the necessary and sufficient conditions for exact factorization $|Psirangle=otimes_p |psi_prangle$ of an eigenstate of a many-body Hamiltonian $H$. The formalism is then used to derive exact dimerization and clusterization conditions in spin systems.
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• Abstract: We derive a general method for determining the necessary and sufficient conditions for exact factorization $|\Psi\rangle=\otimes_p |\psi_p\rangle$ of an eigenstate of a many-body Hamiltonian $H$, based on the quantum covariance matrix of the relevant local operators building the Hamiltonian. The "site" $p$ can be either a single component or a group of subsystems. The formalism is then used to derive exact dimerization and clusterization conditions in spin systems, covering from spin-$s$ singlets and clusters coupled to $0$ total spin to general nonmaximally entangled spin-$s$ dimers (generalized singlets). New results for field induced dimerization in anisotropic $XYZ$ arrays under a magnetic field are obtained.

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