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

C. Marin, A. Fontana, V. Bellani, F. Pederiva, A. Quaranta, F. Rossella, A. Salamon, G. Salina
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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.
用 D-Wave 量子退火器模拟受挫伊辛方阵
在二维(2D)方晶格上具有近邻相互作用的伊辛模型是研究铁磁顶磁转变的最简单模型之一。该模型在理论和数值方面都已成为研究材料磁性相变的典范。在简要回顾了使用经典计算机获得的主要结果之后,我们展示了如何在 D 波量子退火器上实现一个更复杂的伊辛模型,并在对角线近邻之间添加了具有两个耦合常数 J1 和 J2 的竞争性反铁磁相互作用。由于沮度的存在,该系统的动态比简单的伊辛模型更为丰富,除了铁磁相和顺磁相之外,还表现出第三个条纹相(或反铁磁相)。在这项工作中,我们在 D-Wave 硬件上观察到了所有三个相,研究了溶液在不同退火参数(如链强度和退火时间)下的行为,并展示了如何通过改变铁磁耦合和反铁磁耦合之间的比率来识别相变。在经典计算机上研究同一系统时,可以将温度(在 D-Wave 上是固定的)作为自由参数考虑在内,并探索整个相图:得出了一些与 D-Wave 的比较结论。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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