Covariance-based method for eigenstate factorization and generalized singlets
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866909399064248320 |
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| author | Petrovich, Federico Rossignoli, R. Canosa, N. |
| author_facet | Petrovich, Federico Rossignoli, R. Canosa, N. |
| contents | We derive a general method for determining the necessary and sufficient conditions for exact factorization $|Ψ\rangle=\otimes_p |ψ_p\rangle$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_04426 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Covariance-based method for eigenstate factorization and generalized singlets Petrovich, Federico Rossignoli, R. Canosa, N. Quantum Physics Strongly Correlated Electrons We derive a general method for determining the necessary and sufficient conditions for exact factorization $|Ψ\rangle=\otimes_p |ψ_p\rangle$ 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. |
| title | Covariance-based method for eigenstate factorization and generalized singlets |
| topic | Quantum Physics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2311.04426 |