Ground-state properties of quantum triangular ice

Motivated by recent quantum Monte Carlo (QMC) simulations of the quantum Kagome ice model by Juan Carrasquilla et al., [Nat. Commun., 6, 7421 (2015)], we study the ground-state properties of this model on the triangular lattice. In the presence of a magnetic field h, the Hamiltonian possesses competing interactions between a Z(2)-invariant easy-axis ferromagnetic interaction J(+/-+/-) and a frustrated Ising term J(z). As in the U(1)-invariant model, we obtain four classical distinctive phases, however, the classical phases in the Z(2)-invariant model are different. They are as follows: a fully polarized (FP) ferromagnet for large h, an easy-axis canted ferromagnet (CFM) with broken Z(2) symmetry for small h and dominant J(+/-+/-), a ferrosolid phase with broken translational and Z(2) symmetries for small h and dominant J(z), and two lobes with m = < S-z > = +/- 1/6 for small h and dominant J(z). We show that quantum fluctuations are suppressed in this model, hence the large-S expansion gives an accurate picture of the ground-state properties. When quantum fluctuations are introduced, we show that the ferrosolid state is the ground state in the dominant Ising limit at zero magnetic field. It remains robust for J(z) -> 8. With nonzero magnetic field the classical lobes acquire a finite magnetic susceptibility with no S-z order. We present the trends of the ground-state energy and the magnetizations. We also present a detail analysis of the CFM.