Operator renormalization group and spin systems

Calvin Stubbins

doi:10.1103/PhysRevD.44.488

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Operator renormalization group and spin systems

Calvin Stubbins

Department of Physics, Franklin & Marshall College, Lancaster, Pennsylvania

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Phys. Rev. D 44, 488 – Published 15 July, 1991

DOI: https://doi.org/10.1103/PhysRevD.44.488

Abstract

The results of a new hybrid method for calculating ground-state energies for lattice Hamiltonians are presented. This method combines the $t$ expansion with the real-space renormalization-group approach, with the hope of extracting infinite-volume physics at $t \to \infty$ from calculations of only a few powers of $t$ . We calculate the ground-state energy for the (1+1)-dimensional anisotropic Heisenberg model and the (1+1)-dimensional Ising model. Using a blocking that treats the sites and links symmetrically, we were able to determine the exact critical point of the Ising system. In both of these systems we see that the operator renormalization-group method substantially improves upon the results of either the $t$ expansion or real-space renormalization-group methods used separately.

References (14)

D. Horn and M. Weinstein, Phys. Rev. D 30, 1256 (1984)
D. Horn, M. Karliner, and M. Weinstein, Phys. Rev. D 31, 2589 (1985)
C. P. van den Doel and D. Horn, Phys. Rev. D 33, 3011 (1986)
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D. Horn, W. G. J. Langeveld, H. R. Quinn, and M. Weinstein, Phys. Rev. D 38, 3238 (1988)
C. Stubbins, Phys. Rev. D 38, 1942 (1988)
S. D. Drell, M. Weinstein, and S. Yankielowicz, Phys. Rev. D 14, 487 (1976) ibid.14, 1627 (1976)
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[c1] D. Horn and M. Weinstein, Phys. Rev. D 30, 1256 (1984)

[c2] D. Horn, M. Karliner, and M. Weinstein, Phys. Rev. D 31, 2589 (1985)

[c3] C. P. van den Doel and D. Horn, Phys. Rev. D 33, 3011 (1986)

[c4] C. P. van den Doel and D. Horn, Phys. Rev. D 35, 2824 (1987)

[c5] G. J. Mathews, N. J. Snyderman, and S. D. Bloom, Phys. Rev. D 36, 2553 (1987)

[c6] D. Horn, W. G. J. Langeveld, H. R. Quinn, and M. Weinstein, Phys. Rev. D 38, 3238 (1988)

[c7] C. Stubbins, Phys. Rev. D 38, 1942 (1988)

[c8] S. D. Drell, M. Weinstein, and S. Yankielowicz, Phys. Rev. D 14, 487 (1976) ibid.14, 1627 (1976)

[c9] D. Bessis and M. Villani, J. Math. Phys. 16, 462 (1975)

[c10] R. Orbach, Phys. Rev. 112, 309 (1958)

[c11] S. D. Drell, M. Weinstein, and S. Yankielowicz, Phys. Rev. D 16, 1769 (1977)

[c12] P. Pfeuty, Ann. Phys. 57, 79 (1970)

[c13] A. Pacheco, Phys. Rev. D 19, 3173 (1979)

[c14] R. Jullien et al., Phys. Rev. B 38, 3568 (1978)

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Operator renormalization group and spin systems

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