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Separation of spherically and translationally covariant finite quantum spaces within the XXX model

Nuclear physics. B, 2023-06, Vol.991, p.116215, Article 116215 [Peer Reviewed Journal]

2023 The Author(s) ;ISSN: 0550-3213 ;EISSN: 1873-1562 ;DOI: 10.1016/j.nuclphysb.2023.116215

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  • Title:
    Separation of spherically and translationally covariant finite quantum spaces within the XXX model
  • Author: Lulek, T. ; Stagraczyński, R. ; Łabuz, M.
  • Is Part Of: Nuclear physics. B, 2023-06, Vol.991, p.116215, Article 116215
  • Description: A method of separation of subspaces with definite values of the total spin, its z-projection and quasimomentum, within the state space of the XXX model, i.e. the N-th tensor power of a single qubit, is presented. We construct a complete system of orthogonal projectors onto such subspaces by use of the basis of wavelets and chosen measuring operators based on the total spin. We also demonstrate, on examples of N=6 and 8 magnetic spin rings, that the constructed projectors can be further decomposed into the orthogonal sum of density matrices of eigenstates of the XXX model in the corresponding subspaces. This decomposition exhibits a Galois symmetry, stemming from roots of indecomposable factors of characteristic polynomial of the Heisenberg Hamiltonian. In this way, we propose an alternative for Bethe Ansatz for moderate lengths of spin chains, by a return to the original spectral problem, avoiding the highly nonlinear system of Bethe Ansatz equations. Such results are easy to adapt in quantum information processing. •Translational symmetry provides momentum representation of the XXX model.•Jucys – Murphy orthogonal projectors separate exact eigenspaces.•Galois structure of characteristic polynomials yields unification of eigenstates.•Exact density matrices of the XXX model are adapted to quantum information processing.
  • Publisher: Elsevier B.V
  • Language: English
  • Identifier: ISSN: 0550-3213
    EISSN: 1873-1562
    DOI: 10.1016/j.nuclphysb.2023.116215
  • Source: DOAJ Directory of Open Access Journals
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