Quantum critical spin liquids and conformal field theory in 2+1 dimensions

TL;DR

This work introduces infrared fixed points in a 2+1 dimensional quantum field theory built from symplectic fermions, with critical exponents that vary continuously with the number of fermion components $N$ and spacetime dimension $D$. Using a functional RG and Coleman–Weinberg-type effective potential, the authors derive a beta function $d\lambda/d\ell = (4-D)\lambda + (N-4)\lambda^2$ and identify an IR fixed point $\lambda_* = (4-D)/(4-N)$ for $D<4$, which yields nontrivial scaling for the composite order parameter ${\vec n}=χ^ \vec{σ} χ$. For the physically relevant case $N=2$, $D=3$, the exponents are computed to be $\nu=4/5$, $\beta=7/10$, $\eta=3/4$, and $\delta=17/7$, consistent with a deconfined quantum critical point between Néel and VBS-like phases as proposed in the deconfinement framework. The paper also discusses non-unitarity of the theory and proposes a unitary subspace via Hilbert-space projection or a Chern–Simons description, with implications for connections to hedgehog-free $O(3)$ sigma models and potential relevance to cuprate superconductivity. Appendix A provides the key integral evaluation used in the correlation-function analysis.

Abstract

We describe new conformal field theories based on symplectic fermions that can be extrapolated between 2 and 4 dimensions. The critical exponents depend continuously on the number of components N of the fermions and the dimension D. In the context of anti-ferromagnetism, the N=2 theory is proposed to describe a deconfined quantum critical spin liquid corresponding to a transition between a Neel ordered phase and a VBS-like phase.