Point Group Interpretation of Galois Symmetry of Bethe Ansatz Solutions of Magnetic Pentagonal Ring

• Authors: B. Lulek , T. Lulek , M. Łabuz , J. Milewski
• Languages of publication: EN

Abstracts

EN

Exact solutions of the eigenproblem of the magnetic pentagonal ring exhibit the arithmetic symmetry expressed in terms of a Galois group of a finite extension of the prime field Q of rationals. We propose here a geometric interpretation of this symmetry in the interior of the Brillouin zone, in terms of point groups. Explicitly, it is a subgroup of the direct product C₄ × D₄. We present also the appropriate irreducible representations of the group.

Keywords

EN

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

Discipline

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

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2015
• Volume: 127
• Issue: 2
• Pages: 336-338

Dates

published

2015-02

Contributors

author

B. Lulek

• East European State Higher School, T. Terleckiego 6, 37-700 Przemyśl, Poland

author

T. Lulek

• Faculty of Physics, Adam Mickiewicz University, Umultowska 85, 61-614 Poznań, Poland

author

M. Łabuz

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

author

J. Milewski

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

References

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Identifiers

DOI

10.12693/APhysPolA.127.336