“Unnecessary” Quantum Critical Points in Condensed Matter and Field Theory

Quantum critical points usually separate two distinct phases of matter. Here I will discuss a class of "unnecessary" quantum critical points that lie within a single phase of matter (much like the liquid-gas transition, except that they are continuous) so that there is a path that avoids them. First found in critical non-abelian gauge theories, there are by now a number of simpler examples of such quantum critical points. In this talk, I will focus on  the conformal fixed point of massless QED3. I will show that this theory describes an unnecessary quantum critical point living inside the most familiar Neel antiferromagnetic phase of spin-1/2 square lattice magnets.