Abstract
Efficient cluster expansion techniques have been developed for quantum Hamiltonian lattice models. Applications to antiferromagnetic Heisenberg systems, based on expansion about the Ising limit, yield accurate results for both ground state properties and excitation spectra. Recent work on novel systems, including spin ladders and frustrated two-dimensional systems, will be described.
This work forms part of a research project supported by a grant from the Australian Research Council.
Preview
Unable to display preview. Download preview PDF.
References
Affleck, I. (1989): Quantum spin chains and the Haldane gap. J. Phys. Condens. Matter. 1, 3047–3072.
Dagotto, E. and Rice, T.M. (1996): Surprises on the way from one-to two-dimensional quantum magnets — the ladder materials. Science 271, 618–623.
Hamer, C.J., Oitmaa, J., and Zheng, W.H. (1994): Strong-coupling series for Abelian lattice gauge models in 3+1 dimensions. Phys. Rev. D 49, 535–542.
He, H.X., Hamer, C.J. and Oitmaa, J. (1990): High-temperature series expansions for the (2+1)D Ising model. J. Phys. A 23, 1775–1787.
Hornby, P.G. and Barber, M.N. (1985): Perturbation series for the mass gap of the (1+1)-dimensional O(2)-model. J. Phys. A 18, 827–832.
Huse, D.A. (1988): Ground-state staggered magnetization of two-dimensional quantum Heisenberg antiferromangets, Phys. Rev. B 37, 2380–2382.
Gelfand, M.P. (1996): Series expansions for excited states of quantum lattice models, Solid State Communications, 98, 11–14.
Gelfand, M.P., Singh, R.R.P., and Huse, D.A. (1989): Zero-temperature ordering in two-dimensional frustrated quantum Heisenberg antiferromagnet. Phys. Rev. B 40, 10801–10809.
Gelfand, M.P., Singh, R.R.P. and Huse, D.A. (1990): Perturbation expansions for quantum many-body systems. J. of Stat. Phys. 59, 1093–1142.
Gelfand, M.P., et al. (1996): Convergent expansions for properties of the Heisenberg model for CaV4O9, Phys. Rev. Lett. 77, 2794–2797.
Irving, A.C. and Hamer, C.J. (1984): Methods in Hamiltonian lattice field theory (II) Linked-cluster expansions. Nucl. Phys. B230, 361–384.
Hamer, C.J. and Irving, A.C. (1984): Cluster expansions in the (2+1)D Ising model. J. Phys. A 17, 1649–1664.
Manousakis, E. (1991): The spin-1/2 Heisenberg antiferromagnet on a square lattice and its application to the Cuprous Oxides. Rev. Mod. Phys. 63, 1–62.
Marland, L.G., (1981): Series expansions for the zero-temperature transverse Ising model. J. Phys. A 14, 2047–2057.
Martin, J.L. (1974): Phase Transition and Critical Phenomena, Vol. 3 (Domb, C. and Green, M.S., eds., Academic Press).
Nickel, B.G. (1980): unpublished.
Oitmaa, J. and Zheng, W.H. (1996): Series expansion for the J 1 − J 2 Heisenberg antiferromagnet on a square lattice, Phys. Rev. B 54, 3022–3025.
Oitmaa, J., Hamer, C.J., and Zheng, W.H. (1994): Heisenberg antiferromagnet and the XY model at T = 0 in three dimensions. Phys. Rev. B 50, 3877–3893.
Oitmaa, J., Singh, R.R.P., and Zheng, W.H. (1996): Quantum spin ladders at T = 0 and at high temperatures studied by series expansions. Phys. Rev. B 54, 1009–1018.
Rapaport, D.C. (1987): Algorithm for Lattice Statistics. Computer Phys. Rep., 5, 265–349.
Runge, K.J. (1992): Quantum Monte Carlo calculation of the long-range order in the Heisenberg antiferromagnet. Phys. Rev. B 45, 7229–7236.
Schultz, H.J. and Ziman, T.A.L. (1992): Finite-size scaling for the two-dimensional frustrated quantum Heisenberg antiferromagnet. Europhys. Lett. 18, 355–360.
Singh, R.R.P. (1989): Thermodynamic parameters of the T=0, spin-1/2 square-lattice Heisenberg antiferromagnet, Phys. Rev. B 39, 9760–9763.
Singh, R.R.P. (1993): Transverse-spin correlations and single-mode approximation for the square-lattice S=1/2 Heisenberg model. Phys. Rev. B 47, 12337–12340.
Taniguchi, S. et al. (1995): Spin gap behavior of S=1/2 quasi-two-dimensional system CaV4O9, J. Phys. Soc. Jpn. 64, 2758–2761.
Troyer, M., Kontani, H., and Ueda, K. (1996): Phase diagram of depleted Heisenberg model for CaV4O9, Phys. Rev. Lett. 76, 3822–3825.
Zheng, W.H., et al. (1996): Heisenberg models for CaV4O9: expansions about high-temperature, plaquette, Ising, and dimer limits. submitted to Phys. Rev. B.
Zheng, W.H., Oitmaa, J. and Hamer, C.J. (1991): The square-lattice Heisenberg antiferromagnet at T = 0. Phys. Rev. B 43, 8321–8330.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1997 Springer-Verlag
About this paper
Cite this paper
Oitmaa, J., Zheng, W., Hamer, C.J. (1997). Studies of lattice spin systems using series expansions. In: Clark, J.W., Ristig, M.L. (eds) Theory of Spin Lattices and Lattice Gauge Models. Lecture Notes in Physics, vol 494. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0104300
Download citation
DOI: https://doi.org/10.1007/BFb0104300
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-63207-8
Online ISBN: 978-3-540-69211-9
eBook Packages: Springer Book Archive