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Physical review. B, Condensed matter

Equivalence of fractional quantum Hall and resonating-valence-bond states on a square lattice

Z. Zou, Benoît Douçot, B. Sriram Shastry

Published Jun 1, 1989• 34 citations
Publisher

Abstract

We show that a fractional quantum Hall state is equivalent to one particular resonating-valence-bond (RVB) state, the ``flux phase'' on a square lattice. The fictitious magnetic flux is dynamically generated in the RVB state. The fractional quantum Hall wave function for the flux phase is explicitly shown to be a singlet.
DOI
10.1103/physrevb.39.11424

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The ground states of the antiferromagnetic Heisenberg model on the triangular and square lattices are discussed with use of the combinatorial method on the basis of Anderson's RVB (resonating-valence-bond) variational wave-function. Some properties of RVB states are studied systematically for finite system-size N up to 20 and are compared to the exact values. For the triangular lattice the estimated energy value E RVB =-2.08 is closer to the exact value than that of the spin-wave theory. The value E RVB =-2.36 is estimated for the square lattice. For the square lattice our RVB state is closer to the exact ground state than the Néel state is in the sense of a wave-function. The dimer problem has a close relation to RVB states and is used to count exactly the number of singlet-pair configurations.