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Obtaining quantitative ground-state behavior for geometrically-frustratedquantum magnets with long-range interactions is challenging for numericalmethods. Here, we demonstrate that the ground states of these systems ontwo-dimensional lattices can be efficiently obtained using state-of-the-arttranslation-invariant variants of matrix product states and density-matrixrenormalization-group algorithms. We use these methods to calculate thefully-quantitative ground-state phase diagram of the long-range interactingtriangular Ising model with a transverse field on 6-leg infinite-lengthcylinders, and scrutinize the properties of the detected phases. We comparethese results with those of the corresponding nearest neighbor model. Ourresults suggest that, for such long-range Hamiltonians, the long-range quantumfluctuations always lead to long-range correlations, where correlators exhibitpower-law decays instead of the conventional exponential drops observed forshort-range correlated gapped phases. Our results are relevant for comparisonswith recent ion-trap quantum simulator experiments that demonstratehighly-controllable long-range spin couplings for several hundred ions.

Phase diagram of the quantum Ising model with long-range interactions on an infinite-cylinder triangular lattice