XY ring exchange model with frustrated Ising coupling on the triangular lattice

•We study a Z2-invariant XY ring-exchange model on the triangular lattice.•The excitation spectrum is obtained for the pure ring-exchange model.•We discuss possible quantum spin ice and quantum spin liquid phases.

We investigate the nature of a Z2-invariant XY ring-exchange interaction with a frustrated Ising coupling on the triangular lattice. Within the limits of pure XY ring-exchange interaction, we show that the classical ground state is degenerate resulting from the Z2-invariance of the Hamiltonian. Quantum fluctuations lift these classical degenerate ground states and produce an unusual state whose excitation spectrum exhibits a gapped maximum quadratic dispersion near k=0k=0 and vanishes at the midpoints of each side of the Brillouin zone. This result is in contrast to a gapless quadratic dispersion near k=0k=0 in the U(1)-invariant counterpart. We also study the effects of frustration when competing with a classically frustrated Ising interaction. We provide a glimpse into the possible quantum phases that could emerge. A comprehensive understanding of this Hamiltonian, however, cannot be elucidated analytically and requires an explicit numerical simulation.