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Motivated by recent experiments with a Penning ion trap quantum simulator, weperform numerically exact Stochastic Series Expansion quantum Monte Carlosimulations of long-range transverse-field Ising models on a triangular latticefor different decay powers $\alpha$ of the interactions. The phase boundary forthe ferromagnet is obtained as a function of $\alpha$. For antiferromagneticinteractions, there is strong indication that the transverse field stabilizes aclock ordered phase with sublattice magnetization $(M,-\frac{M}{2},-\frac{M}{2})$ with unsaturated $M < 1$ in a process known as "order bydisorder" similar to the nearest neighbour antiferromagnet on the triangularlattice. Connecting the known limiting cases of nearest neighbour andinfinite-range interactions, a semiquantitative phase diagram is obtained.Magnetization curves for the ferromagnet for experimentally relevant systemsizes and with open boundary conditions are presented.

Quantum Monte Carlo Study of Long-Range Transverse-Field Ising Models on the Triangular Lattice