Quantum Spin Liquid with Even Ising Gauge Field Structure on Kagome Lattice

Employing large-scale quantum Monte Carlo simulation, we study the extended XXZ model on kagome lattice. A $\mathbb Z_2$ quantum spin liquid phase with effective even Ising gauge field structure emerges from the delicate balance among three symmetry breaking phases including stripe solid, staggered solid and ferromagnetic phase. This $\mathbb Z_2$ spin liquid is beyond the Lieb-Schultz-Mattis-Oshikawa-Hastings theorem and made possible by the introduction of an extended interaction related to Rokhsar-Kivelson potential. The phase transitions from staggered solid to spin liquid and ferromagnetic phase are first order, so is the transition between stripe solid and ferromagnetic phase. However, the transition between spin liquid and ferromagnetic phase is found to be continuous and belong to 3D XY$^*$ universality class associated with the condensation of spinons, and the transition between spin liquid and stripe solid is seemingly continuous and associated with the condensation of visons.