Emergent Rokhsar-Kivelson point in realistic quantum Ising models

We demonstrate that in triangular lattice quantum Ising antiferromagnets, the seemingly trivial first-order transition between the clock and stripe phases is associated with quantum critical behaviors. This phase transition is driven by proliferation of domain walls between clock domains, where the domain wall tension vanishes at the critical point. We present its relation to the Rokhsar-Kivelson deconfined quantum critical point in quantum dimer models. We discuss experimental signatures of this quantum critical point. We propose that such critical point may be realized in the rare-earth material TmMgGaO₄ by applying hydrostatic pressure. We also discuss potential experimental realization in programmable Rydberg arrays.