Covariance-based method for eigenstate factorization and generalized singlets

Abstract

We derive a general method for determining the necessary and sufficient conditions for exact factorization |Ψ⟩=⊗_|_⟩ of an eigenstate of a many-body Hamiltonian , based on the quantum covariance matrix of the relevant local operators building the Hamiltonian. The “site” 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- singlets and clusters coupled to 0 total spin, to general nonmaximally entangled spin- dimers (generalized singlets). New results for field-induced dimerization in anisotropic ⁢⁢ arrays under a magnetic field are obtained.