Matrix Representation of Constants of Motion for One-Dimensional Heisenberg Magnet

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

Abstracts

EN

We demonstrate an exact diagonalization of the one-dimensional Heisenberg magnet in terms of algebraic Bethe Ansatz. We point out, by a polynomial expansion of the transfer matrix with respect to spectral parameter, a complete set of observables for classification of all eigenstates. We introduce an application of our approach on the example of the Heisenberg magnet consisting of four qubits, including its constants of motion, density matrices and complete classification of eigenstates.

Keywords

EN

03.65.Aa; 75.10.Jm

Discipline

• 03.65.Aa: Quantum systems with finite Hilbert space
• 75.10.Jm: Quantized spin models, including quantum spin frustration

• Journal: Acta Physica Polonica A
• Year: 2015
• Volume: 128
• Issue: 2
• Pages: 176-178

Dates

published

2015-08

Contributors

author

P. Jakubczyk

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

author

M. Labuz

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

author

T. Lulek

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

References

• [1] R.J. Baxter, Ann. Phys. 70, 323 (1972), doi: 10.1016/0003-4916(72)90270-9
• [2] B. Sutherland, J. Math. Phys. 11, 3183 (1970), doi: 10.1063/1.1665111
• [3] L.D. Faddeev, L.A. Takhtajan, J. Sov. Math. 24, 241 (1984), doi: 10.1007/BF01087245
• [4] P.A.M. Dirac, Phys. Today 11, 32 (1958), doi: 10.1063/1.3062610
• [5] H. Bethe, Z. Phys. 71, 205 (1931) (in German; English translation in: D.C. Mattis, The Many-Body Problem, World Sci., Singapore 1993, p. 689), doi: 10.1007/BF01341708

Identifiers

DOI

10.12693/APhysPolA.128.176