Zero-temperature properties of the long-range transverse-field Ising model on the triangular lattice

We investigate the ground state properties of the transverse-field Ising model with long-range, antiferromagnetic interactions on the triangular lattice. Our study is motivated by experiments on trapped beryllium ions, where the ions form a 2D Wigner crystal with tunable 1/r^α Ising interactions in the range 0 ≤ α ≤ 3, where r is the distance between two spins. Our results are obtained using a projector variant of the stochastic series expansion (SSE) Monte Carlo method, which allows direct access to ground state properties throughout the phase diagram.