Application of Contractor Renormalization Group to the Heisenberg Zig-Zag and the Hubbard Chain

• Authors: K. Cichy , P. Tomczak
• Languages of publication: EN

Abstracts

EN

The contractor renormalization group method was devised in 1994 by Morningstar and Weinstein. It was primarily aimed at extracting the physics of lattice quantum field theories (like lattice quantum chromodynamics). However, it is a general method of analyzing Hamiltonian lattice systems, e.g. Ising, Heisenberg or Hubbard models. The aim of this work is to show the application of contractor renormalization group method to one-dimensional quantum systems - the Heisenberg zig-zag model and the Hubbard chain. As a test of the method, the ground state energy of these systems will be calculated.

Keywords

EN

05.10.Cc; 03.65.Fd; 75.10.Jm; 71.10.Fd

Discipline

• 71.10.Fd: Lattice fermion models (Hubbard model, etc.)
• 03.65.Fd: Algebraic methods(see also 02.20.-a Group theory)
• 75.10.Jm: Quantized spin models, including quantum spin frustration
• 05.10.Cc: Renormalization group methods

• Journal: Acta Physica Polonica A
• Year: 2007
• Volume: 111
• Issue: 5
• Pages: 773-780

Dates

published

2007-05

Contributors

author

K. Cichy

• Institute of Physics, A. Mickiewicz University, Umultowska 85, 61-614 Poznań, Poland

author

P. Tomczak

• Institute of Physics, A. Mickiewicz University, Umultowska 85, 61-614 Poznań, Poland

References

• 1. C. Morningstar, M. Weinstein, Phys. Rev. Lett., 73, 1873, 1994
• 2. C. Morningstar, M. Weinstein, Phys. Rev. D, 54, 4131, 1996
• 3. J. Piekarewicz, J.R. Shepard, Phys. Rev. B, 56, 5366, 1997
• 4. J. Piekarewicz, J.R. Shepard, Phys. Rev. B, 57, 10260, 1998
• 5. M. Weinstein, Phys. Rev. B, 63, 174421, 2001
• 6. E. Berg, E. Altman, A. Auerbach, Phys. Rev. Lett., 90, 147204, 2003
• 7. R. Budnik, A. Auerbach, Phys. Rev. Lett., 93, 187205, 2004
• 8. S. Capponi, A. Lauchli, M. Mambrini, Phys. Rev. B, 70, 104424, 2004
• 9. P. Li, S.-Q. Shen, Phys. Rev. B, 71, 212401, 2005
• 10. E. Altman, A. Auerbach, Phys. Rev. B, 65, 104508, 2002
• 11. S. Capponi, D. Poilblanc, Phys. Rev. B, 66, 180503, 2002
• 12. H.A. Bethe, Z. Phys., 71, 205, 1931
• 13. L. Hulthén, Arkiv. Nat. Astron. Fys. A, 26, no. 11, 1, 1938
• 14. P.W. Anderson, Phys. Rev., 86, 694, 1952
• 15. E.H. Lieb, F.Y. Wu, Phys. Rev. Lett., 20, 1445, 1968

Identifiers

DOI

10.12693/APhysPolA.111.773