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Prog. Theor. Phys. Vol. 85 No. 3 (1991) pp. 481-492

Transfer-Matrix Calculations of the Spin 1/2 Antiferromagnetic XXZ Model on the 4 ×2 Triangular Lattice Using the Fractal Decomposition

Naomichi Hatano and Masuo Suzuki

Department of Physics, University of Tokyo, Tokyo 113

(Received November 7, 1990)

Abstract:

The fractal decomposition of exponential operators proposed by Suzuki, which is a new category of the generalized Trotter decomposition valid up to higher orders, is examined with transfer-matrix calculations of the spin 1/2 antiferromagnetic XXZ model on the 4 ×2 triangular lattice. The dependence of correction terms on the Trotter number and temperature are studied. This dependence confirms rapid convergence of the fractal decomposition. The negative-sign problem arising in quantum Monte Carlo simulations is also discussed from the present new point of view.

URL : http://ptp.ipap.jp/link?PTP/85/481/
DOI : 10.1143/PTP.85.481

[ Full Text PDF : FREE ACCESS (533K) ] Citation: Plain Text BiBTeX EndNote(RIS) RSS

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References:

1. Quantum Monte Carlo Methods, ed. M. Suzuki (Springer-Verlag, Berlin, 1987).
2. M. Suzuki, J. Stat. Phys. 43 (1986), 883, and references cited therein.
3. M. Suzuki, Phys. Lett. A146 (1990), 319; J. Math. Phys. 32 (1991), 400[CrossRef].
4. M. Takasu, S. Miyashita and M. Suzuki, in Ref. 1).
5. N. Hatano and M. Suzuki, to be published in Phys. Lett. A.
6. E. Y. Loh, J. E. Gubernatis, R. T. Scaletter, S. R. White, D. J. Scalapino and R. L. Sugar, Phys. Rev. B41 (1990), 9301[APS].
7. D. R. Hamann and S. B. Fahy, Phys. Rev. B41 (1990), 11352[APS].
8. S. Sorella, Preprint, S.I.S.S.A. 147 CM (Dec. 89).
9. N. Furukawa and M. Imada, J. Phys. Soc. Jpn. 60 (1991), 810[JPSJ].

Citing Article(s) :

1. Journal of the Physical Society of Japan 61 (1992) pp. 3015-3019 :

   General Nonsymmetric Higher-Order Decomposition of Exponential Operators and Symplectic Integrators

   Masuo Suzuki

2. Journal of the Physical Society of Japan 63 (1994) pp. 1691-1697 :

   Data Analysis for Quantum Monte Carlo Simulations with the Negative-Sign Problem

   Naomichi Hatano

3. Journal of the Physical Society of Japan 81 (2012) 104002 (17 pages) :

   The Fermionic Minus-Sign Problem for the Ground State, Revisited with Higher Order Suzuki–Trotter Decompositions

   Xiaoxing Wang and Hans-Georg Matuttis

4. Progress of Theoretical Physics Supplement No.138 (2000) pp. 489-494 :

   Quantum Statistical Mechanics on a Quantum Computer

   H. De Raedt, A. H. Hams, K. Michielsen, S. Miyashita and K. Saito

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