We revisit the challenging problem of identifying the quantum spin liquid candidate in the spin-1/2 $J_1\text{−}{J}_2$ 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 ${\mathrm{Z}}_2$ 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 ${\mathrm{Z}}_2$ and U(1) parton state, we investigate the chiral spin liquid ground states as topological orders by incorporating a $J_{\chi }$ term into the $J_1\text{−}{J}_2$ model and observe a transition from a ${\mathrm{Z}}_2$ chiral spin liquid to a $\mathrm{U}{\left(1\right)}_2$ chiral spin liquid as $J_{\chi }$ increases.

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• Density matrix renormalization group
• Dirac fermions
• Frustrated magnetism
• Quantum spin liquid
• Topological order
• Gauge symmetries
• Heisenberg model
• Projective symmetries