Geodesic
On a Complete Basis in the Space of Rotationally Invariant Operators of $N$ Quantum Spins $1/2$
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Mathematics of Quantum Technologies, Tome 313 (2021), pp. 280-284

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Systems of quantum spins $1/2$ with isotropic Heisenberg interaction play an important role in physics. In studying such systems, it may be useful to have a complete, yet non-overcomplete, basis of operators each of which has the symmetry of the Hamiltonian, i.e., is invariant with respect to rotations (global $\mathrm {SU}(2)$ transformations of the Pauli matrices). This paper presents an algorithm for constructing such a basis. The algorithm is implemented in Wolfram Mathematica.
Mots-clés : Pauli matrices
Keywords: isotropic Heisenberg interaction, quantum spin systems, operator basis. 
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     author = {F. G. Uskov},
     title = {On a {Complete} {Basis} in the {Space} of {Rotationally} {Invariant} {Operators} of $N$ {Quantum} {Spins} $1/2$},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
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F. G. Uskov. On a Complete Basis in the Space of Rotationally Invariant Operators of $N$ Quantum Spins $1/2$. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Mathematics of Quantum Technologies, Tome 313 (2021), pp. 280-284. http://geodesic.mathdoc.fr/item/TM_2021_313_a23/