Quantum Monte Carlo Study of Long-Range Transverse-Field Ising Models on the Triangular Lattice

TL;DR

This paper uses quantum Monte Carlo simulations to explore phase diagrams and magnetic ordering in long-range transverse-field Ising models on a triangular lattice, relevant to recent ion trap experiments.

Contribution

It provides the first numerically exact phase diagram for long-range transverse-field Ising models on a triangular lattice, including effects of decay power and boundary conditions.

Findings

Phase boundary for ferromagnetic interactions as a function of decay power α.

Evidence that transverse field stabilizes a clock ordered phase in antiferromagnetic case.

Magnetization curves relevant to experimental system sizes.

Abstract

Motivated by recent experiments with a Penning ion trap quantum simulator, we perform numerically exact Stochastic Series Expansion quantum Monte Carlo simulations of long-range transverse-field Ising models on a triangular lattice for different decay powers $\alpha$ of the interactions. The phase boundary for the ferromagnet is obtained as a function of $\alpha$. For antiferromagnetic interactions, there is strong indication that the transverse field stabilizes a clock ordered phase with sublattice magnetization $(M,-\frac{M}{2}, -\frac{M}{2})$ with unsaturated $M < 1$ in a process known as "order by disorder" similar to the nearest neighbour antiferromagnet on the triangular lattice. Connecting the known limiting cases of nearest neighbour and infinite-range interactions, a semiquantitative phase diagram is obtained. Magnetization curves for the ferromagnet for experimentally relevant system sizes and with open boundary conditions are presented.