Quantum order-by-disorder in the triangular lattice long-range Ising model

Recent advances in ion traps have enabled a broader range of quantum simulations on static 2D lattices. These experiments can stabilize a triangular lattice with long-range Ising interactions between spin qubits, where the purely classical model exhibits geometric frustration giving rise to extensively many low-energy states. Using the density matrix renormalization group (DMRG), we numerically study the lifting of the extensive classical ground state degeneracy via small quantum fluctuations. In this regime, there are two competing ordered phases, either an "up-up-down" or a "clock" ordering pattern. Strong boundary effects arising from the power-law interactions make numerical studies highly challenging, and have led to a mysterious region at very low but nonzero field which appears to be dominated by classical stripes. We further investigate the fate of this model in this limit.