Valence bond description of the long-range, nonfrustrated Heisenberg chain
Abstract
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).
Keywords
Cite
@article{arxiv.0709.4487,
title = {Valence bond description of the long-range, nonfrustrated Heisenberg chain},
author = {K. S. D. Beach},
journal= {arXiv preprint arXiv:0709.4487},
year = {2007}
}
Comments
4 pages, 6 figures