Chiral Symmetry Breaking, Deconfinement and Entanglement Monotonicity

TL;DR

This paper uses the F-theorem and entanglement entropy to derive non-perturbative bounds on fermion flavors for QED-3 stability and constrains quantum critical points with topological order.

Contribution

It applies the generalized c-theorem to strongly interacting theories, deriving bounds on fermion flavors and insights into quantum critical points using entanglement entropy.

Findings

Bounds on fermion flavors for QED-3 stability

Constraints on quantum critical points with topological order

Utilization of entanglement entropy ratios in theoretical bounds

Abstract

We employ the recent results on the generalization of the $c$-theorem to 2+1-d to derive non-perturbative results for strongly interacting quantum field theories, including QED-3 and the critical theory corresponding to certain quantum phase transitions in condensed matter systems. In particular, by demanding that the universal constant part of the entanglement entropy decreases along the renormalization group flow ("F-theorem"), we find bounds on the number of flavors of fermions required for the stability of QED-3 against chiral symmetry breaking and confinement. In this context, the exact results known for the entanglement of superconformal field theories turn out to be quite useful. Furthermore, the universal number corresponding to the ratio of the entanglement entropy of a free Dirac fermion to that of free scalar plays an interesting role in the bounds derived. Using similar ideas, we also derive strong constraints on the nature of quantum critical points in condensed matter systems with "topological order".