I. G. Bostrem, A. S. Ovchinnikov, V. E. Sinitsyn, “The method of exact diagonalization preserving the total spin and taking the point symmetry of the two-dimensional isotropic Heisenberg magnet into account”, TMF, 149:2 (2006), 262–280; Theoret. and Math. Phys., 149:2 (2006), 1527

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Teoreticheskaya i Matematicheskaya Fizika, 2006, Volume 149, Number 2, Pages 262–280
DOI: https://doi.org/10.4213/tmf4233 (Mi tmf4233)

This article is cited in 11 scientific papers (total in 11 papers)

The method of exact diagonalization preserving the total spin and taking the point symmetry of the two-dimensional isotropic Heisenberg magnet into account

I. G. Bostrem, A. S. Ovchinnikov, V. E. Sinitsyn

Ural State University

Full-text PDF (436 kB) Citations (11)

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DOI: https://doi.org/10.4213/tmf4233

Abstract: We propose a double-pass method of exact diagonalization of a finite cluster on the base of functions that have a definite total spin and transform by a definite irreducible representation of the point symmetry group of the lattice. We also propose the method for approximating the energy spectrum in the thermodynamic limit using the spectrum of the surrounding states, which increases the calculation accuracy leaving the cluster size invariant. The algorithm details are extensively illustrated with an example of clusters of spin $1/2$ on a simple square lattice.

Keywords: Heisenberg model, exact diagonalization, cluster calculations, group theory, angular momentum theory, two-dimensional antiferromagnet.

Received: 17.04.2006

English version:
Theoretical and Mathematical Physics, 2006, Volume 149, Issue 2, Pages 1527–1544
DOI: https://doi.org/10.1007/s11232-006-0136-z

Bibliographic databases:

Language: Russian

Citation: I. G. Bostrem, A. S. Ovchinnikov, V. E. Sinitsyn, “The method of exact diagonalization preserving the total spin and taking the point symmetry of the two-dimensional isotropic Heisenberg magnet into account”, TMF, 149:2 (2006), 262–280; Theoret. and Math. Phys., 149:2 (2006), 1527–1544

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Linking options:

https://www.mathnet.ru/eng/tmf4233

https://doi.org/10.4213/tmf4233

https://www.mathnet.ru/eng/tmf/v149/i2/p262

This publication is cited in the following 11 articles:

Werner Dobrautz, Vamshi M. Katukuri, Nikolay A. Bogdanov, Daniel Kats, Giovanni Li Manni, Ali Alavi, “Combined unitary and symmetric group approach applied to low-dimensional Heisenberg spin systems”, Phys. Rev. B, 105:19 (2022)
Seki K., Shirakawa T., Yunoki S., “Symmetry-Adapted Variational Quantum Eigensolver”, Phys. Rev. A, 101:5 (2020), 052340
Heitmann T., Schnack J., “Combined Use of Translational and Spin-Rotational Invariance For Spin Systems”, Phys. Rev. B, 99:13 (2019), 134405
Oliver Hanebaum, Jürgen Schnack, “Advanced finite-temperature Lanczos method for anisotropic spin systems”, Eur. Phys. J. B, 87:9 (2014)
Schnack J., Ummethum J., “Advanced Quantum Methods for the Largest Magnetic Molecules”, Polyhedron, 66:SI (2013), 28–33
A. S. Ovchinnikov, I. G. Bostrem, Vl. E. Sinitsyn, “Cluster perturbation theory for spin Hamiltonians”, Theoret. and Math. Phys., 162:2 (2010), 179–187
Khamzin A.M., Nigmatullin R.R., “Magnetic properties of magnetoactive spin clusters”, Journal of Experimental and Theoretical Physics, 111:6 (2011), 1028–1038
Schnalle R., Schnack J., “Calculating the energy spectra of magnetic molecules: application of real- and spin-space symmetries”, International Reviews in Physical Chemistry, 29:3 (2010), 403–452
Irene G. Bostrem, Alexander S. Ovchinnikov, Valentine E. Sinitsyn, “Application of Symmetry Methods to Low-Dimensional Heisenberg Magnets”, Symmetry, 2:2 (2010), 722
Schnalle, R, “Numerically exact and approximate determination of energy eigenvalues for antiferromagnetic molecules using irreducible tensor operators and general point-group symmetries”, Physical Review B, 79:10 (2009), 104419
Schnalle, R, “Approximate eigenvalue determination of geometrically frustrated magnetic molecules”, Condensed Matter Physics, 12:3 (2009), 331

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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