  Obtaining quantitative ground-state behavior for geometrically-frustrated
quantum magnets with long-range interactions is challenging for numerical
methods. Here, we demonstrate that the ground states of these systems on
two-dimensional lattices can be efficiently obtained using state-of-the-art
translation-invariant variants of matrix product states and density-matrix
renormalization-group algorithms. We use these methods to calculate the
fully-quantitative ground-state phase diagram of the long-range interacting
triangular Ising model with a transverse field on 6-leg infinite-length
cylinders, and scrutinize the properties of the detected phases. We compare
these results with those of the corresponding nearest neighbor model. Our
results suggest that, for such long-range Hamiltonians, the long-range quantum
fluctuations always lead to long-range correlations, where correlators exhibit
power-law decays instead of the conventional exponential drops observed for
short-range correlated gapped phases. Our results are relevant for comparisons
with recent ion-trap quantum simulator experiments that demonstrate
highly-controllable long-range spin couplings for several hundred ions.
