Heisenberg and Bethe Field Extensions Applied to Magnetic Rings

• Authors: G. Banaszak , D. Blinkiewicz , P. Krasoń , J. Milewski
• Languages of publication: EN

Abstracts

EN

We consider striking connections between the theory of homogenous isotropic Heisenberg ring (XXX-model) and algebraic number theory. We explain the nature of these connections especially applications of Galois theory for computation of the spectrum of the Heisenberg operators and Bethe parameters. The solutions of the Heisenberg eigenproblem and Bethe Ansatz generate interesting families of algebraic number fields. Galois theory yields additional symmetries which not only simplify the analysis of the model but may lead to new applications and horizons.

Keywords

EN

02.10.De; 03.65; 73.21.-b; 75.10.Jm; 85.35.Be; 89.70.Be

Discipline

• 85.35.Be: Quantum well devices (quantum dots, quantum wires, etc.)
• 02.10.De: Algebraic structures and number theory
• 75.10.Jm: Quantized spin models, including quantum spin frustration
• 73.21.-b: Electron states and collective excitations in multilayers, quantum wells, mesoscopic, and nanoscale systems(for electron states in nanoscale materials, see 73.22.-f)

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2018
• Volume: 133
• Issue: 3
• Pages: 441-443

Dates

published

2018-03

Contributors

author

G. Banaszak

• Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614 Poznań, Poland

author

D. Blinkiewicz

• Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614 Poznań, Poland

author

P. Krasoń

• Department of Mathematics and Physics, Szczecin University, Wielkopolska 15, 70-415 Szczecin, Poland

author

J. Milewski

• Institute of Mathematics, Poznań University of Technology, Piotrowo 3A, 60-965 Poznań, Poland

References

• [1] G. Banaszak, S. Barańczuk, T. Lulek, J. Milewski, R. Stagraczy, 121, 1111 (2012), doi: 10.12693/APhysPolA.121.1111
• [2] J. Milewski, G. Banaszak, T. Lulek, M. Łabuz, R. Stagraczyński, Open Syst. Inf. Dyn. 19, 1250012 (2012), doi: 10.1142/S1230161212500126
• [3] G. Banaszak, B. Lulek, T. Lulek, J. Milewski, B. Szydło, Rep. Math. Phys. 71, 205 (2013), doi: 10.1016/S0034-4877(13)60030-0
• [4] J. Milewski, Rep. Math. Phys. 70, 345 (2012), doi: 10.1016/S0034-4877(12)60050-0
• [5] S.V. Kerov, A.N. Kirillov, N.Y. Reshetikhin, J. Sov. Math. 41, 916 (1988), doi: 10.1007/BF01247087
• [6] A.N. Kirillov, N.Y. Reshetikhin, J. Sov. Math. 41, 925 (1988), doi: 10.1007/BF01247088
• [7] R. Langlands, Y. Saint-Aubin, Aspects combinatoires des équations de Bethe, First appeared in Adv. Math. Sci.: CRM's 25 years, Ed. L. Vinet, CRM Proc. and Lecture Notes, Am. Math. Soc., 1997 http://sunsite.ubc.ca/DigitalMathArchive/Langlands/pdf/bethe-ps.pdf
• [8] R. Langlands, Y. Saint-Aubin, Algebro-geometric aspects of the Bethe equations, Proc. of Gürsey Memorial Conference, Springer-Verlag 1995, doi: 10.1007/3-540-59163-X_254
• [9] P. Krasoń, J. Milewski, Cyclic group actions and restricted partitions, preprint (2017)
• [10] J. Milewski, G. Banaszak, T. Lulek, Open Syst. Inf. Dyn. 17, 89 (2010), doi: 10.1142/S1230161210000072
• [11] H. Bethe: Z. Physik 71, 205 (1931), doi: 10.1007/BF01341708

Identifiers

DOI

10.12693/APhysPolA.133.441