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We show that several distinct broken-symmetry phases in a spin-1/2anti-ferromagnet on a square lattice with easy-plane anisotropy, includingvalence bond solid, chiral spin liquid, and the XY-ordered state, can all beaccessed by perturbing a multi-critical point with two massless Dirac fermionscoupled to a level-one Chern-Simons gauge field. This allows for a unifieddescription of these phases, as well as the phase transitions between them. Ina specific phase transition our analysis provide a lattice realization of oneof the recently proposed fermion-boson duality, thus lending support to it. Wealso briefly discuss the relation between our work and the long-soughtde-confined criticality in such systems.

Multi-critical point and unified description of broken-symmetry phases in spin-1/2 anti-ferromagnets on a square lattice