Abstract
A generalization of the Niemeijer and Van Leeuwen real-space renormalization group method for quantum lattice spin systems is presented. A proposed rotationally invariant transformation which preserves the symmetry of the spin space is applied to several quantum systems on a triangular lattice. For the spin-1/2XY-model in both first- and second-order cumulant expansions a nontrivial fixed point exists, giving in the best approximation a critical interactionK cXY =0.453 and critical exponent ν=1.65. A method of the reduction of the generalized arbitrary spin anisotropic Heisenberg model to the spin-half model is presented.
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Betts, D.D., Tsai, J.T., Elliott, C.J.: Proceedings of the ICM, Moscow 1973. Vol. IV, p. 279. Moscow: Nauka 1974
Goldhirsch, I., Levich, E., Yakhot, V.: Phys. Lett.62 A, 273 (1977)
Niemeijer, Th., Van Leeuwen, J.M.J.: Physica71, 17 (1974)
Rogiers, J., Dekeyser, R.: Phys. Rev. B13, 4886 (1976)
Betts, D.D., Plischke, M.: Can. J. Phys.15, 1553 (1976)
Rogiers, J., Betts, D.D.: Physica A85, 553 (1976)
Brower, R.C., Kuttner, F., Nauenberg, M., Subbarao, K.: Phys. Rev. Lett.38, 1231 (1977)
Stella, A.L., Toigo, F.: Phys. Rev. B17, 2343 (1978)
Stella, A.L., Vanderzande, C., Dekeyser, R.: Phys. Rev. B27, 1812 (1983)
Dekeyser, R., Reynaert, M., Stella, A.L., Toigo, F.: Phys. Rev. B18, 3486 (1978)
Suzuki, M., Takano, H.: Phys. Lett.69 A, 426 (1979)
Takano, H., Suzuki, M.: J. Stat. Phys.26, 635 (1981)
Barma, M., Kumar, D., Pandey, R.B.: J. Phys. C12, L 909 (1979)
Castellani, C., Di Castro, C., Ranninger, J.: Nucl. Phys. B200 [FS4], 45 (1982)
See, e.g., Wilcox, R.M.: J. Math. Phys.8, 962 (1967)
Penson, K.A., Jullien, R., Pfeuty, P.: Phys. Rev. B22, 380 (1980)
Stella, A.L., Toigo, F.: Physica89 A, 175 (1977)
Austen, D.J., Plischke, M.: Phys. Lett. A48, 47 (1974)
Berker, A.N.: Phys. Rev. B12, 2752 (1975)
Sznajd, J.: Phys. Status Solidi (b)124, 103 (1984)
Rogiers, J., Grundke, E.W., Betts, D.D.: Can. J. Phys.57, 1719 (1979)
Kosterlitz, J.M., Thouless, D.: J. Phys. C6, 1181 (1973)
Zittartz, J.: Z. Phys. B — Condensed Matter23, 55, 63 (1976)
Berezinskii, V.L.: Sov. Phys. — JETP32, 493 (1970);34, 610 (1971)
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Sznajd, J. Real-space renormalization group for two-dimensional quantum spin systems. Z. Physik B - Condensed Matter 62, 349–355 (1986). https://doi.org/10.1007/BF01313458
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DOI: https://doi.org/10.1007/BF01313458