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arXiv · 1802.00422

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

S. N. Saadatmand·S. D. Bartlett·I. P. McCulloch
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Abstract

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.

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S. N. Saadatmand, S. D. Bartlett, I. P. McCulloch. 2019-04-03. Phase diagram of the quantum Ising model with long-range interactions on an infinite-cylinder triangular lattice. https://doi.org/10.1103/physrevb.97.155116

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