Dirac and chiral spin liquids on spin-1/2 square-lattice Heisenberg antiferromagnet

Abstract: We revisit the challenging problem of identifying the quantum spin liquid candidate in the spin-1/2 $J_1$-$J_2$ Heisenberg antiferromagnet on the square lattice. By integrating the Gutzwiller-guided density matrix renormalization group method with analytical analyses, we present clear evidence that the ground state is a Z$2$ Dirac spin liquid. This state can be efficiently described by a Gutzwiller-projected parton theory characterized by its projective symmetry group. To distinguish the difference between the projected Z$_2$ and U(1) parton state, we investigate the chiral spin liquid ground states as topological orders by incorporating a $J\chi$ term into the $J_1$-$J_2$ model and observe a transition from a Z$2$ chiral spin liquid to a U(1)$_2$ chiral spin liquid as $J\chi$ increases.