Comment on “Gapless spin liquid ground state of the spin- 12 J1−J2 Heisenberg model on square lattices”

Liu et al. [Phys. Rev. B 98, 241109 (2018)] used Monte Carlo sampling of the physical degrees of freedom of a projected entangled pair state type wave function for the S=1/2 frustrated J1−J2 Heisenberg model on the square lattice and found a nonmagnetic state argued to be a gapless spin liquid when the coupling ratio g=J2/J1 is in the range g∈[0.42,0.6]. Here we show that their definition of the order parameter for another candidate ground state within this coupling window—a spontaneously dimerized state—is problematic. The order parameter as defined will not detect dimer order when lattice symmeties are broken due to open boundaries or asymmetries originating from the calculation itself. Thus, a dimerized phase for some range of g cannot be excluded (and is likely based on several other recent works).Accepted manuscrip