Valence bond description of the long-range, nonfrustrated Heisenberg chain

Details Valence bond description of the long-range, nonfrustrated Heisenberg chain Valence bond description of the long-range, nonfrustrated Heisenberg chain

2007-09-27

arxiv.org/abs/0709.4487v1

Physics

Condensed Matter

Strongly Correlated Electrons

4 pages, 6 figures

Scientific paper

The Heisenberg chain with antiferromagnetic, powerlaw exchange has a quantum phase transition separating spin liquid and Neel ordered phases at a critical value of the powerlaw exponent alpha. The behaviour of the system can be explained rather simply in terms of a resonating valence bond state in which the amplitude for a bond of length r goes as r^{-alpha} for alpha < 1, as r^{-(1+alpha)/2} for 1 < alpha < 3, and as r^{-2} for alpha > 3. Numerical evaluation of the staggered magnetic moment and Binder cumulant reveals a second order transition at alpha_c = 2.18(5), in excellent agreement with quantum Monte Carlo. The divergence of the magnetic correlation length is consistent with an exponent nu = 2/(3-alpha_c) = 2.4(2).

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