Abstract
Comparisons are made between several different linked-cluster expansion methods, namely the linked-cluster perturbation series expansion, the t-expansion, the analytic Lanczos expansion, and the coupled-cluster expansion. They are considered from a technical point of view, and also as applied to the S=1/2 Heisenberg antiferromagnet on the square lattice and the compact U(1) lattice gauge model in 2+1 dimensions.
This work forms part of a research project supported by a grant from the Australian Research Council.
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References
Banks, T., Myerson, R. and Kogut, J. (1977): Phase transitions in Abelian lattice gauge theories. Nucl. Phys. B129, 493–510.
Barnes T. (1991): The 2D Heisenberg antiferromagnetic in high-Tc superconductivity, a review of numerical techniques and results. Int. J. Mod. Phys. C2, 659–709.
Bishop, R.F. (1991): An overview of coupled cluster theory and its applications in physics. Theor. Chim. Acta 80, 95–148.
Coester, F., and Kümmel, H. (1960): Short-range correlations in nuclear wave functions. Nucl. Phys. 17, 477–485.
Domb, C. and Green, M.S. (1974): Phase Transitions and Critical Phenomena. Vol. 3.
Fang, X.Y., Liu, J.M. and Guo, S.H. (1996): Vacuum wave function and mass gaps of U(1) lattice gauge theory in 2+1 dimensions. Phys. Rev. D 53 1523–1527
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. (1990): Perturbation expansions for quantum many-body systems. J. of Stat. Phys. 59, 1093–1142.
Gross, L.G. (1983): Convergence of U(1)3 lattice gauge theory to its continuum limit. Commun. Math. Phys. 92, 137–162.
Guo, S.H., Chen, Q.Z. and Li, L. (1994): Analytic calculation of the vacuum wave function for (2+1)-dimensional SU(2) lattice gauge theory. Phys. Rev. D 49, 507–510.
Göpfert, M. and Mack, G. (1982): Proof of confinement of static Quarks in 3-dimensional U(1) lattice gauge theory for all values of the coupling constant. Commun. Math. Phys. 82, 545–606.
Hamer, C.J., Oitmaa, J. and Zheng, W.H. (1992): Series analysis of U(1) and SU(2) lattice gauge theory in 2+1 dimensions. Phys. Rev. D 45, 4652–4658.
Hamer, C.J., Wang, K.C. and Price, P.F. (1994): Finite-size scaling for the U(1) lattice gauge model in 2+1 dimensions. Phys. Rev. D 50, 4693–4702.
Hamer, C.J. and Zheng, W.H. (1993): Weak-coupling expansions and effective lagrangian for compact U(1) lattice gauge theory in D+1 dimensions. Phys. Rev. D 48, 4435–4449.
Hamer, C.J., Zheng, W.H. and Oitmaa, J. (1994): Spin-wave stiffness of the Heisenberg antiferromagnet at zero temperature. Phys. Rev. B 50, 6877–6888.
Hamer, C.J., Zheng, W.H. and Oitmaa, J. (1996): Comparison between linked-cluster expansion methods for the U(1) lattice gauge model in 2+1 dimensions. Phys. Rev. D 53, 1429–1438.
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.
Hollenberg, L.C.L. and Witte, N.S. (1994): General nonperturbative estimate of the energy density of lattice Hamiltonians. Phys. Rev. D 50, 3382–3386.
Horn, D. and Weinstein, M., (1984): The t expansion: a nonperturbative analytic tool for Hamiltonian systems. Phys. Rev. D 30, 1256–1270.
Irving, A.C. and Hamer, C.J., (1984): Methods in Hamiltonian lattice field theory (II) Linked-cluster expansions. Nucl. Phys. B230, 361–384.
Nickel, B.G. (1980): unpublished.
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.
Morningstar, C.J. (1992): Bistate t-expansion study of U(1) lattice gauge theory in 2+1 dimensions. Phys. Rev. D46, 824–835.
Polyakov, A.M. (1977): Quark confinement and topology of gauge theories. Nucl. Phys. B120, 429–458.
Runge, K.J. (1992): Finite-size study of the ground state energy, susceptibility, and spin-wave velocity for the Heisenberg antiferromagnet. Phys. Rev. B 45, 12292–12296.
Schreiber, D. (1994): t-expansion of heavy-light mesons, Phys. Rev. D 49, 2567–2573.
Smith, C.H.L and Watson, N.J (1993): The shifted coupled cluster method. A new approach to Hamiltonian lattice gauge theories. Phys. Lett. B302, 463–471.
Witte, N.S., Hollenberg, L.C.L. and Zheng, W.H. (1996): 2D XXZ model ground state Properties using an analytic Lanczos expansion. submitted to Phys. Rev. B.
Zeng, C., Farnell, D.J.J. and Bishop, R.F. (1996): An efficient implementation of high-order coupled-cluster techniques applied to quantum magnets. cond-mat/9611012.
Zheng, W.H. and Hamer, C.J. (1993): Spin-wave theory and finite-size scaling for the Heisenberg antiferromagnet. Phys. Rev. B 47, 7961–7970.
Zheng, W.H., Oitmaa, J. and Hamer, C.J. (1991): The square-lattice Heisenberg anti-ferromagnet at T = 0. Phys. Rev. B 43, 8321–8330.
Zheng, W.H., Oitmaa, J., and Hamer, C.J. (1995): Comparison between linked-cluster expansion methods for the Heisenberg antiferromagnet on the square lattice. Phys. Rev. B 52, 10278–10285.
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Zheng, W., Hamer, C.J., Oitmaa, J. (1997). Application of linked-cluster expansions to quantum hamiltonian lattice systems. 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/BFb0104301
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DOI: https://doi.org/10.1007/BFb0104301
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