Towards Spin-Wave Like Approach to the J-J' Heisenberg Antiferromagnet in Terms of Composite Spins

• Authors: P. Grzybowski , R. Chhajlany
• Languages of publication: EN

Abstracts

EN

Conventional spin-wave approach relies on an expansion around a relevant classical (unentangled) ground state or equivalently the ground state in the mean field approximation for the quantum model. However, for systems which may admit valence bond ground states, such as the staggered J-J' Heisenberg antiferromagnet, single site mean field approximation is obviously an incorrect zeroth order approximation. In this paper, we introduce a mean field approximation for clusters consisting of two spins connected by a strong bond in the aforementioned model. We identify the quantum critical point and calculate the ground state magnetization within this cluster mean field approximation in one and two dimensions. Finally, we derive an effective dimer Hamiltonian, in the standard basis operator formalism, which may be a basis for further spin-wave like expansions around the cluster mean field approximation ground state.

Keywords

EN

75.10.Jm; 75.50.Ee; 75.40.Cx

Discipline

• 75.50.Ee: Antiferromagnetics
• 75.40.Cx: Static properties (order parameter, static susceptibility, heat capacities, critical exponents, etc.)
• 75.10.Jm: Quantized spin models, including quantum spin frustration

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2009
• Volume: 115
• Issue: 1
• Pages: 168-170

Dates

published

2009-01

Contributors

author

P. Grzybowski

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

author

R. Chhajlany

• Institute of Physics, Adam Mickiewicz University, Umultowska 85, PL-61-614 Poznań, Poland
• Faculty of Applied Physics and Mathematics, Gdańsk University of Technology, 80-952 Gdańsk, Poland
• National Quantum Information Centre of Gdańsk, 81-824 Sopot, Poland

References

• 1. D. Yoshioka, G. Arakawa, I. Ichinose, T. Matsui, Phys. Rev. B 70, 174407 (2004)
• 2. S. Wenzel, L. Bogacz, W. Janke, arXiv:0805.2500 (2008)
• 3. R.R.P. Singh, M.P. Gelfand, D.A. Huse, Phys. Rev. Lett. 61, 2484 (1988)
• 4. N.B. Ivanov, S.E. Kruger, J. Richter, Phys. Rev. B 53, 2633 (1996)
• 5. S.E. Kruger, J. Richter, J. Schulenburg, D.J.J. Farnell, R.F. Bishop, Phys. Rev. B 61, 14607 (2000)
• 6. P. Tomczak, J. Richter, J. Phys. A, Math. Gen. 34, L461 (2001)
• 7. S.B. Haley, P. Erdös, Phys. Rev. B 5, 1106 (1972)
• 8. P.R. Grzybowski, R. W. Chhajlany, in preparation

Identifiers

DOI

10.12693/APhysPolA.115.168