Magnetic Pentagonal Ring - Galois Extensions and Crystallography

• Authors: M. Labuz , T. Lulek
• Languages of publication: EN

Abstracts

EN

The Galois symmetry of exact Bethe Ansatz eigenstates for magnetic pentagonal ring is shown to bear a close analogy to some crystallographic constructions. Automorphisms of number field extensions associated with these eigenstates prove to be related to choices of the Bravais cells in the finite crystal lattice ℤ₂×ℤ₂, responsible for extension of the cyclotomic field by the Bethe parameters.

Keywords

EN

75.10.Jm; 03.65.Fd; 03.67.Lx; 02.10.Ud; 02.10.De

Discipline

• 02.10.Ud: Linear algebra
• 03.65.Fd: Algebraic methods(see also 02.20.-a Group theory)
• 02.10.De: Algebraic structures and number theory
• 03.67.Lx: Quantum computation architectures and implementations
• 75.10.Jm: Quantized spin models, including quantum spin frustration

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2017
• Volume: 132
• Issue: 1
• Pages: 97-99

Dates

published

2017-07

Contributors

author

M. Labuz

• Department of Theoretical Physics, Faculty of Mathematics and Natural Sciences, University of Rzeszów, S. Pigonia 1, 35-310 Rzeszów, Poland

author

T. Lulek

• Faculty of Physics, Adam Mickiewicz University, Umultowska 85, 61-614 Poznań, Poland
• Department of Experimental Physics, Faculty of Mathematics and Natural Sciences, University of Rzeszów, S. Pigonia 1, 35-310 Rzeszów, Poland

References

• [1] W. Hao, R.I. Nepomechie, A.J. Sommese, Phys. Rev. E 88, 052113 (2013)., doi: 10.1103/PhysRevE.88.052113
• [2] J. Milewski, G. Banaszak, T. Lulek, M. Łabuz, R. Stagraczyński, OSID 19, 1250012 (2012)., doi: 10.1142/S1230161212500126
• [3] J. Milewski, G. Banaszak, T. Lulek, M. Labuz, Physica B 406, 520 (2011)., doi: 10.1016/j.physb.2010.11.027
• [4] H. Bethe, Z. Phys. 71, 205 (1931) (in German, doi: 10.1007/BF01341708
• [4a] English translation: D.C. Mattis, The Many-Body Problem, World Sci., Singapore 1993, p. 689., doi: 10.1142/9789812796523
• [5] G. Banaszak, B. Lulek, T. Lulek, J. Milewski, B. Szydło, ROMP 71, 205 (2013)., doi: 10.1016/S0034-4877(13)60030-0
• [6] S. Lang, Algebra, Addison-Wesley World Student Series, Reading (MA) 1970.
• [7] J. Mozrzymas, Applications of Group Theory in Physics, PWN, Warsaw 1977 (in Polish)
• [8] J. Mozrzymas, ROMP 6, 29 (1974)., doi: 10.1016/0034-4877(74)90049-4
• [8a] J. Mozrzymas, ROMP 6, 83 (1974)., doi: 10.1016/0034-4877(74)90050-0
• [9] B. Lulek, T. Lulek, M. Łabuz, R. Stagraczyński, Physica B 405, 2654 (2010)., doi: 10.1016/j.physb.2010.03.043
• [10] P. Jakubczyk, A. Wal, D. Jakubczyk, T. Lulek, Comp. Phys. Commun. 183, 1354 (2012)., doi: 10.1016/j.cpc.2012.01.025

Identifiers

DOI

10.12693/APhysPolA.132.97