Quantum critical scaling behavior of deconfined spinons

TL;DR

This paper analyzes the critical behavior of deconfined spinons in various quantum antiferromagnetic models using renormalization group techniques, providing evidence for deconfined quantum criticality in certain cases and calculating critical exponents.

Contribution

It demonstrates that deconfined spinons are critical in isotropic SU(N) models for large N and possibly down to N=2, and explores the conditions under which deconfined quantum criticality occurs or fails.

Findings

Deconfined spinons are critical for large N in SU(N) Heisenberg antiferromagnets.

Deconfined quantum criticality likely persists down to N=2 in certain models.

The critical exponent η is calculated to first order in ε for models exhibiting deconfined criticality.

Abstract

We perform a renormalization group analysis of some important effective field theoretic models for deconfined spinons. We show that deconfined spinons are critical for an isotropic SU(N) Heisenberg antiferromagnet, if $N$ is large enough. We argue that nonperturbatively this result should persist down to N=2 and provide further evidence for the so called deconfined quantum criticality scenario. Deconfined spinons are also shown to be critical for the case describing a transition between quantum spin nematic and dimerized phases. On the other hand, the deconfined quantum criticality scenario is shown to fail for a class of easy-plane models. For the cases where deconfined quantum criticality occurs, we calculate the critical exponent $\eta$ for the decay of the two-spin correlation function to first-order in $\epsilon=4-d$. We also note the scaling relation $\eta=d+2(1-\phi/\nu)$ connecting the exponent $\eta$ for the decay to the correlation length exponent $\nu$ and the crossover exponent $\phi$.