An exact upper bound for the ground-state energy of the triangular antiferromagnetic lattice by means of a renormalization procedure

Braak, H.; Caspers, W.J.; Willemse, M.W.M.

doi:10.1016/0375-9601(78)90048-8

Cited by 8 publications

(1 citation statement)

References 6 publications

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“…This cluster has been used in ref. [2] for the calculation of an upper bound (-1.820) for E. Let K be given by 7 6 K(7) = i=2 ~ S1 " Si + 7 i~= 2 Si " Si + l + 7S2"$7.…”

Section: Consider the Following Cluster 7mentioning

confidence: 99%

Lower bounds for the ground state energy of spin systems

Broek

1981

Physics Letters A

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“…This cluster has been used in ref. [2] for the calculation of an upper bound (-1.820) for E. Let K be given by 7 6 K(7) = i=2 ~ S1 " Si + 7 i~= 2 Si " Si + l + 7S2"$7.…”

Section: Consider the Following Cluster 7mentioning

confidence: 99%

Lower bounds for the ground state energy of spin systems

Broek

1981

Physics Letters A

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Many-body valence-bond theory

Klein

Zhu

Valentí

et al. 1997

Int. J. Quant. Chem.

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ABSTRACT:The classical theory of chemical valence, first, is naturally formalized in mathematics in the area of graph theory and, second, finds an extension in quantum Ž . mechanics in terms of the Heitler᎐London᎐Pauling '' valence-bond'' VB theory. Thus, VB theory stands in a fairly unique position, although in quantum chemistry, there often Ž . has been a preference for the alternative perhaps even ''complementary'' molecular Ž . orbital MO theory, presumably in large part because of computational efficacy for general molecular structures. Indeed, as formulated by Pauling and others, VB theory Ž . was described as a configuration interaction CI problem when there were multiple relevant classical valence structures for the same molecular structure. Also, as now recognized, a direct assault on CI is computationally intensive, prone to size-inconsistency problems, and effectively limited to smaller systems-whereas indirect approaches, e.g., via wave-function cluster expansions or renormalization-group theory, often neatly avoid Ž . these problems. Thus, what is and perhaps always has been needed is ''many-body'' Ž . schemes for VB computations as well as for higher-order MO-based approaches, too . Here, then, certain such many-body VB-amenable computational schemes are to be Ž . discussed, in the context of semiempirical explicitly correlated graphical models. The collection of models are described and interrelated in a fairly comprehensive systematic manner. A selection of many-body cluster expansion methods are then discussed with special reference to resonating VB wave functions and the fundamental graph-theoretic Ž nature of the consequent problems such as also are noted to arise in lattice-discretized . statistical-mechanical problems, too . Some examples are described incorporating resonance among exponentially great numbers of VB structures as applied: for large Ž . icosahedral-symmetry fullerenic structures, for the polyacetylenic linear chain, and for ladderlike conjugated polymers. It is contended that practicable many-body VB-theoretic methods are now available, retaining clear links to classical chemical valence theory. Hopefully, too, these methods may soon find use beyond the semi-empirical framework.

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Renormalization techniques for quantum spin systems. Ground-state energies

Caspers

1980

Physics Reports

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Introduction and general outline of the method 225 3. Examples. Ising and isotropic XY systems with a transverse 2. Examples. Systems without external magnetic field 229 magnetic field 251 2.1. Linear chain with nearest and next-nearest neighbour 4. Concluding remarks 256 interactions; first order 230 Appendix A: Algebraic properties of the spin 257 2.2. Peierls-distorted chain 232 Appendix B: Kramers' theorem 259 2.3. Triangular lattice 238 Appendix C: The Wigner-Eckart theorem 261 2.4. Linear chain; variational method 240 References 262 2.5. Linear chain; second order 244

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An exact upper bound for the ground-state energy of the triangular antiferromagnetic lattice by means of a renormalization procedure

Abstract: A renormalization procedure gives a rigorous upper bound for the ground-state energy per spin for the triangular antiferromagnetic lattice with Heisenberg interaction.

Cited by 8 publications

References 6 publications

Lower bounds for the ground state energy of spin systems

Lower bounds for the ground state energy of spin systems

Many-body valence-bond theory

Renormalization techniques for quantum spin systems. Ground-state energies

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