Title: Modeling a frustrated Ising square lattice with the D-Wave Quantum Annealer Show Chinese title

Title: 用D-Wave量子退火器对受挫的伊辛正方形晶格进行建模

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. Show Chinese abstract

Abstract: 伊辛模型在二维（2D）正方形晶格上具有最近邻相互作用，是研究铁磁到顺磁转变的最简单的模型之一。 文献中已有大量关于该模型的结果，该模型已成为研究材料中磁相变的典范，无论是理论上还是数值上。 在简要回顾了经典计算机获得的主要结果后，我们展示了如何在D-Wave量子退火器上实现一个更复杂的伊辛模型，该模型增加了对角线次近邻之间的竞争反铁磁相互作用，并有两个耦合常数J1和J2。 由于挫败，该系统的动力学比简单伊辛模型更丰富，并且除了铁磁和顺磁相外，还表现出第三种条纹（或反铁磁）相。 在本工作中，我们在D-Wave硬件上观察到了所有三种相，研究了不同退火参数（如链强度和退火时间）下解决方案的行为，并展示了如何通过改变铁磁和反铁磁耦合之间的比例来识别相变。 同一系统在经典计算机上进行研究，可以将温度（在D-Wave上固定）作为自由参数并探索完整的相图：得出了与D-Wave的一些比较结论。