Fractal valence bond loops in a long-range Heisenberg model at criticality

Details Fractal valence bond loops in a long-range Heisenberg model at criticality Fractal valence bond loops in a long-range Heisenberg model at criticality

2007-07-02

arxiv.org/abs/0707.0297v1

Physics

Condensed Matter

Strongly Correlated Electrons

4 + epsilon pages, 3 figures

Scientific paper

We present a valence bond theory of the spin-S quantum Heisenberg model. For nonfrustracting, local exchange and dimension d > 1, it predicts a resonating ground state with bond amplitudes h(r) ~ (a^2+r^2)^(-p/2) and decay exponent p=d+1. Different values of p can be achieved by introducing frustrating (p > d+1) or nonfrustrating (p < d+1) long-range interactions. For d=2, but not d=3, there is a critical value of the decay exponent p_c above which the ground state is a spin liquid. The phase transition is analogous to quantum percolation, with fractal valence bond loops playing the role of percolating clusters. The critical exponents are continuously tunable along the phase boundary p=p_c(a,S).

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