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Nuclear Physics B

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

Tadeusz Lulek, Ryszard Stagraczyński, M. Łabuz

Published Apr 28, 2023• 1 citation

Abstract

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.

DOI: 10.1016/j.nuclphysb.2023.116215

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