Comment on "Gapless spin liquid ground state of the spin-$\frac{1}{2}$ $J_1$-$J_2$ Heisenberg model on square lattices"

Abstract

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 (PEPS) type wave function for the $S=1/2$ frustrated $J_1$-$J_2$ Heisenberg model on the square lattice and found a non-magnetic state argued to be a gapless spin liquid when the coupling ratio $g=J_2/J_1$ is in the range $g\in [0.42,0.6]$. 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).

arXiv comment4 pages, 5 figures

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• Valence-bond solids, vestigial order, and emergent SO(5) symmetry in a two-dimensional quantum magnet
• Emergent O(4) symmetry at the phase transition from plaquette-singlet to antiferromagnetic order in quasi-two-dimensional quantum magnets
• Plaquette-type valence bond solid state in the $J_1$-$J_2$ square-lattice Heisenberg model
• Reply to comments on "Gapless spin liquid ground state of spin-1/2 $J_1$-$J_2$ Heisenberg model on square lattices"
• Field-induced states and thermodynamics of the frustrated Heisenberg antiferromagnet on a square lattice