Dirac spin liquids (DSLs) are a class of gapless quantum spin ?liquids. In square lattice spin-1/2 magnets? DSL is described at low ?energies by (2+1)d quantum electrodynamics with 4 flavors of massless ?Dirac fermions minimally coupled to an emergent U(1) gauge field.

The existence of a relevant, symmetry-allowed monopole perturbation? ?renders the DSL on the square lattice intrinsically unstable.

We argue that the DSL describes a stable continuous phase transition ?within the familiar Neel phase (or within the Valence Bond Solid (VBS) ?phase). In other words, the DSL is an ``unnecessary'' quantum critical ?point within a single phase of matter.

Our result offers a novel view of the square lattice DSL in that the ?critical spin liquid can exist within either the Neel or VBS state ?itself, and does not require leaving these conventional states.?

On kagome lattices, we analyze a system of SU(3) fermions which may ?realize a DSL phase, described quantum electrodynamics with 6 Dirac fermions.?

We conclude that the low energy DSL is also intrinsically unstable ?due to a relevant monopole perturbation that is a singlet under all ?physical symmetries.

By analyzing the anomalies of the DSL critical point and neighboring ?phases, we also argue the DSL is an unnecessary quantum critical ?point, lying completely within a single phase.