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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2021, Volume 313, Pages 280–284
DOI: https://doi.org/10.4213/tm4194 (Mi tm4194) 		 
This article is cited in 1 scientific paper (total in 1 paper)

On a Complete Basis in the Space of Rotationally Invariant Operators of $N$ Quantum Spins $1/2$

F. G. Uskov

Skolkovo Institute of Science and Technology, Bol'shoi bul. 30, stroenie 1, Moscow, 121205 Russia
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DOI: https://doi.org/10.4213/tm4194
Abstract: 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.
Keywords: Pauli matrices, isotropic Heisenberg interaction, quantum spin systems, operator basis.
Funding agency Grant number
Russian Foundation for Basic Research 18-32-20218
This work was supported by the Russian Foundation for Basic Research, project no. 18-32-20218.
Received: August 24, 2020
Revised: September 11, 2020
Accepted: October 29, 2020
English version:
Proceedings of the Steklov Institute of Mathematics, 2021, Volume 313, Pages 263–267
DOI: https://doi.org/10.1134/S0081543821020243
Bibliographic databases:
Document Type: Article
UDC: 517.958:530.145:512
Language: Russian
Citation: F. G. Uskov, “On a Complete Basis in the Space of Rotationally Invariant Operators of $N$ Quantum Spins $1/2$”, Mathematics of Quantum Technologies, Collected papers, Trudy Mat. Inst. Steklova, 313, Steklov Math. Inst., Moscow, 2021, 280–284; Proc. Steklov Inst. Math., 313 (2021), 263–267
Citation in format AMSBIB
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\inbook Mathematics of Quantum Technologies
\bookinfo Collected papers
\serial Trudy Mat. Inst. Steklova
\yr 2021
\vol 313
\pages 280--284
\publ Steklov Math. Inst.
\publaddr Moscow
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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