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

TL;DR

This paper develops a valence bond theory for the quantum Heisenberg model, revealing a critical phase with fractal valence bond loops and tunable critical exponents influenced by long-range interactions.

Contribution

It introduces a novel valence bond framework predicting fractal loops and criticality in long-range Heisenberg models, extending understanding of quantum spin liquids.

Findings

Ground state exhibits bond amplitudes decaying as (a^2+r^2)^(-p/2)

Critical decay exponent p_c determines phase transition to spin liquid

Fractal valence bond loops are key to the critical behavior

Abstract

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).