Combined use of translational and spin-rotational invariance for spin systems

Heitmann T, Schnack J (2019)
PHYSICAL REVIEW B 99(13): 134405.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor/in
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Abstract / Bemerkung
Exact diagonalization and other numerical studies of quantum spin systems are notoriously limited by the exponential growth of the Hilbert space dimension with system size. A common and well-known practice to reduce this increasing computational effort is to take advantage of the translational symmetry CN in periodic systems. This represents a rather simple yet elegant application of the group theoretical symmetry projection operator technique. For isotropic exchange interactions, the spin-rotational symmetry SU(2) can be used, where the Hamiltonian matrix is block structured according to the total spin and magnetization quantum numbers. Rewriting the Heisenberg Hamiltonian in terms of irreducible tensor operators allows for an efficient and highly parallelizable implementation to calculate its matrix elements recursively in the spin-coupling basis. When combining both CN and SU(2), mathematically, the symmetry projection technique leads to ready-to-use formulas. However, the evaluation of these formulas is very demanding in both computation time and memory consumption, problems which are said to outweigh the benefits of the symmetry-reduced matrix shape. We show a way to minimize the computational effort for selected systems and present the largest numerically accessible cases.
Erscheinungsjahr
2019
Zeitschriftentitel
PHYSICAL REVIEW B
Band
99
Ausgabe
13
Art.-Nr.
134405
ISSN
2469-9950
eISSN
2469-9969
Page URI
https://pub.uni-bielefeld.de/record/2935404

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Heitmann T, Schnack J. Combined use of translational and spin-rotational invariance for spin systems. PHYSICAL REVIEW B. 2019;99(13): 134405.
Heitmann, T., & Schnack, J. (2019). Combined use of translational and spin-rotational invariance for spin systems. PHYSICAL REVIEW B, 99(13), 134405. doi:10.1103/PhysRevB.99.134405
Heitmann, T., and Schnack, J. (2019). Combined use of translational and spin-rotational invariance for spin systems. PHYSICAL REVIEW B 99:134405.
Heitmann, T., & Schnack, J., 2019. Combined use of translational and spin-rotational invariance for spin systems. PHYSICAL REVIEW B, 99(13): 134405.
T. Heitmann and J. Schnack, “Combined use of translational and spin-rotational invariance for spin systems”, PHYSICAL REVIEW B, vol. 99, 2019, : 134405.
Heitmann, T., Schnack, J.: Combined use of translational and spin-rotational invariance for spin systems. PHYSICAL REVIEW B. 99, : 134405 (2019).
Heitmann, Tjark, and Schnack, Jürgen. “Combined use of translational and spin-rotational invariance for spin systems”. PHYSICAL REVIEW B 99.13 (2019): 134405.