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

TL;DR

This paper maps the phase diagram of a long-range interacting quantum Ising model on a triangular lattice using advanced tensor network methods, revealing persistent long-range correlations due to quantum fluctuations.

Contribution

It introduces efficient tensor network algorithms for studying long-range quantum magnets on 2D lattices and provides the first quantitative phase diagram for this system.

Findings

Long-range quantum fluctuations induce power-law correlations.

The phase diagram differs significantly from the nearest-neighbor model.

Results are relevant for ion-trap quantum simulations.

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.