Modeling a frustrated Ising square lattice with the D-Wave Quantum Annealer

TL;DR

This paper demonstrates how to implement a frustrated Ising model with competing interactions on a D-Wave quantum annealer, revealing rich phase behavior including a third striped phase, and compares quantum and classical simulation results.

Contribution

It introduces a method to simulate a frustrated Ising model with next-nearest neighbor interactions on D-Wave hardware, exploring phase transitions and comparing with classical computations.

Findings

All three magnetic phases observed on D-Wave hardware.

Solution behavior varies with annealing parameters like chain strength and time.

Phase transition identified by changing the ratio of coupling constants.

Abstract

The Ising model with nearest-neighbor interactions on a two-dimensional (2D) square lattice is one of the simplest models for studying ferro-magnetic to para-magnetic transitions. Extensive results are available in the literature for this model, which has become a paradigm for the study of magnetic phase transitions in materials, both theoretically and numerically. After a brief review of the main results obtained with a classical computer, we show how to implement on the D- Wave quantum annealer a more complex Ising model with the addition of competing antiferromagnetic interactions between the diagonal next-to-nearest neighbors with two coupling constants J1 and J2. The dynamics of this system, owing to frustration, are richer than those of the simple Ising model and exhibit a third striped (or antiferromagnetic) phase in addition to the ferro- and para-magnetic phases. In this work, we observed all three phases on the D-Wave hardware, studied the behavior of the solution with different annealing parameters, such as the chain strength and annealing time, and showed how to identify the phase transition by varying the ratio between the ferromagnetic and antiferromagnetic couplings. The same system is studied on a classical computer, with the possibility of taking into account the temperature (fixed on D-Wave) as a free parameter and to explore the full phase diagram: some comparative conclusions with D-Wave are drawn.