Continuous phase transition between N\'eel and spin liquid states with topological order

It is well known that on square lattice N\'eel and valence bond solid states are connected by a continuous phase transition, and the critical theory consists fractionalized spinons and an emergent U(1) gauge field. Motivated by recent numerical works revealing N\'eel and gapped spin liquid states in $J_1$-$J_2$ model on square lattice, we study other phases that can be obtained after destroying the N\'eel order. We show that by condensing fields that carry both electric charge and magnetic flux of the emergent gauge field, one can obtain spin liquid phases with topological order and no lattice symmetry breaking.