The Hilbert Space and the Exact Solution of the Spin-Electron Double-Tetrahedral Chain

• Authors: D. Jakubczyk , L. Gálisová
• Languages of publication: EN

Abstracts

EN

We discuss an exactly solvable double-tetrahedral chain, in which the localized Ising spins regularly alternate with triangular clusters - each available for one mobile electron. We give an exact solution for the considered hybrid system by the construction of the N-th tensor power of the Fourier transformation and using the generalized decoration-iteration mapping tranformation.

Keywords

EN

02.20.-a; 05.30.-d; 75.10.Pq; 05.50.+q

Discipline

• 75.10.Pq: Spin chain models
• 05.30.-d: Quantum statistical mechanics(for quantum fluids aspects, see 67.10.Fj)
• 05.50.+q: Lattice theory and statistics (Ising, Potts, etc.)(see also 64.60.Cn Order-disorder transformations, and 75.10.Hk Classical spin models)
• 02.20.-a: Group theory(for algebraic methods in quantum mechanics, see 03.65.Fd; for symmetries in elementary particle physics, see 11.30.-j)

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2015
• Volume: 128
• Issue: 2
• Pages: 173-175

Dates

published

2015-08

Contributors

author

D. Jakubczyk

• Department of Physics, Rzeszów University of Technology, al. Powstańców Warszawy 6, 35-959 Rzeszów, Poland

author

L. Gálisová

• Department of Applied Mathematics and Informatics, Faculty of Mechanical Engineering, Technical University, Letná 9, 042 00 Košice, Slovak Republic

References

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• [4] S.R.J.F. Clark, Strongly Correlated One-Dimensional Systems of Cold Atoms in Optical Lattices, Trinity College, Oxford 2007
• [5] L. Gálisová, J. Strečka, arXiv: 1408.1207
• [6] B. Lulek, T. Lulek, A. Wal, P. Jakubczyk, Physica B 337, 375 (2003), doi: 10.1016/S0921-4526(03)00430-7
• [7] D. Jakubczyk, Acta Phys. Pol. B 44, 1921 (2013), doi: 10.5506/APhysPolB.44.1921
• [8] P. Jakubczyk, S. Topolewicz, A. Wal, Open Syst. Inform. Dyn. 16, 221 (2009), doi: 10.1142/S1230161209000165
• [9] J. Strečka, On the Theory of Generalized Algebraic Transformations, LAP LAMBERT Academic Publishing, Saarbrücken 2010
• [10] D.A. Lavis, G.M. Bell, Statistical Mechanics of Lattice Systems, Vol. 1, Springer, Oxford 1999

Identifiers

DOI

10.12693/APhysPolA.128.173