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

TL;DR

This paper critiques previous claims of a gapless spin liquid in the $J_1$-$J_2$ Heisenberg model, highlighting issues with the order parameter used and suggesting a dimerized phase cannot be ruled out.

Contribution

It identifies problems with the order parameter definition in prior work, challenging the conclusion of a gapless spin liquid and supporting the possibility of a dimerized phase.

Findings

Order parameter used in prior work is problematic.

Dimerized phase cannot be excluded within the coupling window.

Lattice symmetry breaking affects detection of dimer order.

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).