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The behavior of the number of inequivant sites as a function of the spin sector arises from the presence of an additional permutation symmetry among the sites for the 27-site cluster with the chosen boundary conditions. This symmetry does not in general commute with the two reflection symmetries of the cluster, and so cannot be obtained simultaneously with these. However, in the majority of spin sectors it is possible to obtain all three symmetries simultaneously, making sites i = 2 and 3, i = 5 and 5′, and i = 4 and 7 equivalent in these cases
-
The behavior of the number of inequivant sites as a function of the spin sector arises from the presence of an additional permutation symmetry among the sites for the 27-site cluster with the chosen boundary conditions. This symmetry does not in general commute with the two reflection symmetries of the cluster, and so cannot be obtained simultaneously with these. However, in the majority of spin sectors it is possible to obtain all three symmetries simultaneously, making sites i = 2 and 3, i = 5 and 5′, and i = 4 and 7 equivalent in these cases.
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A further heuristic justification for the relevance of the current results at least to the S = 3/2 case may be obtained by considering that the kagome geometry supports a nondegenerate valence-bond-solid state (Ref. 27) for spins S = 2. In a RVB basis a system of spins S = 3/2 is equivalent to a set of dimer vacancies in this background which have exactly the same degeneracy as the dimers in the S = 1/2 system
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A further heuristic justification for the relevance of the current results at least to the S = 3/2 case may be obtained by considering that the kagome geometry supports a nondegenerate valence-bond-solid state (Ref. 27) for spins S = 2. In a RVB basis a system of spins S = 3/2 is equivalent to a set of dimer vacancies in this background which have exactly the same degeneracy as the dimers in the S = 1/2 system.
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Reexamination of results obtained by two of the authors (Ref. 19) reveals that a mutual repulsion of impurities also occurs in the spin chain with frustrating next-neighbor interactions
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Reexamination of results obtained by two of the authors (Ref. 19) reveals that a mutual repulsion of impurities also occurs in the spin chain with frustrating next-neighbor interactions.
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