Geodesic
The method of exact diagonalization preserving the total spin and
Teoretičeskaâ i matematičeskaâ fizika, Tome 149 (2006) no. 2, pp. 262-280
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We propose a double-pass method of exact diagonalization of a finite cluster on the base of functions that have a definite total spin and transform by a definite irreducible representation of the point symmetry group of the lattice. We also propose the method for approximating the energy spectrum in the thermodynamic limit using the spectrum of the surrounding states, which increases the calculation accuracy leaving the cluster size invariant. The algorithm details are extensively illustrated with an example of clusters of spin $1/2$ on a simple square lattice.
Keywords: Heisenberg model, exact diagonalization, cluster calculations, group theory, angular momentum theory
Mots-clés : two-dimensional antiferromagnet. 
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I. G. Bostrem; A. S. Ovchinnikov; V. E. Sinitsyn. The method of exact diagonalization preserving the total spin and. Teoretičeskaâ i matematičeskaâ fizika, Tome 149 (2006) no. 2, pp. 262-280. http://geodesic.mathdoc.fr/item/TMF_2006_149_2_a7/

[1] E. Dagotto, Rev. Mod. Phys., 66 (1994), 763 | DOI

[2] S. R. White, Phys. Rev. Lett., 69 (1992), 2863 ; Phys Rev. B, 48 (1993), 10345 | DOI | DOI

[3] I. Peschel, X. Wang, M. Kaulke, K. Hallberg (eds), Density-Matrix Renormalization. A New Numerical Method in Physics (Lectures of a seminar and workshop held at the Max-Planck-Institut für Physik komplexer Systeme), Lect. Notes Phys., 528, Springer, Berlin, 1999 | DOI | MR | Zbl

[4] U. Schollwöck, Rev. Mod. Phys., 77 (2005), 259 | DOI | MR | Zbl

[5] G. Sierra, T. Nishino, Nucl. Phys. B, 495 (1997), 505 | DOI | MR | Zbl

[6] W. Tatsuaki, Phys. Rev. E, 61 (2000), 3199 | DOI

[7] I. P. McCulloch, M. Gulasci, Austral. J. Phys., 53 (2000), 597 | Zbl

[8] I. P. McCulloch, M. Gulasci, Europhys. Lett., 57 (2002), 852 | DOI

[9] S. Ostlund, S. Rommer, Phys. Rev. Lett., 75 (1995), 3537 ; Phys Rev. B, 55 (1997), 2164 | DOI | DOI

[10] J. Dukelsky, M. A. Martin-Delgado, T. Nishino, G. Sierra, Europhys. Lett., 43 (1998), 457 | DOI

[11] J. M. Roman, G. Sierra, J. Dukelsky, M. A. Martin-Delgado, J. Phys. A, 31 (1998), 9729 | DOI | MR | Zbl

[12] D. D. Betts, H. Q. Lin, J. S. Flyn, Can. J. Phys., 77 (1999), 353 | DOI

[13] G. F. Koster, J. O. Dimmock, R. G. Wheeler, H. Statz, Properties of the Thirty-Two Point Groups, MIT Press, Cambridge, MA, 1963 | MR

[14] D. A. Varshalovich, A. N. Moskalev, V. K. Khersonskii, Kvantovaya teoriya uglovogo momenta, Nauka, L., 1975 | MR | Zbl

[15] D. J. J. Farnell, Phys. Rev. B, 68 (2003), 134419 | DOI

[16] A. W. Sandvik, Phys. Rev. B, 56 (1997), 11678 | DOI

[17] J. S. Griffith, The Irreducible Tensor Method for Molecular Symmetry Groups, Prentice-Hall, Englewood Cliffe, NJ, 1962