20,373 research outputs found
The Wiener and Terminal Wiener indices of trees
Heydari \cite{heydari2013} presented very nice formulae for the Wiener and
terminal Wiener indices of generalized Bethe trees. It is pity that there are
some errors for the formulae. In this paper, we correct these errors and
characterize all trees with the minimum terminal Wiener index among all the
trees of order and with maximum degree .Comment: 13 page
SU(3) trimer resonating-valence-bond state on the square lattice
We propose and study an SU(3) trimer resonating-valence-bond (tRVB) state
with point-group symmetry on the square lattice. By devising a
projected entangled-pair state representation, we show that all (connected)
correlation functions between local operators in this SU(3) tRVB state decay
exponentially, indicating its gapped nature. We further calculate the modular
and matrices by constructing all nine topological sectors on a torus
and establish the existence of topological order in this SU(3)
tRVB state.Comment: 6 pages, 6 figure
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