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arXiv 0705.1643cond-mat.str-elcond-mat.stat-mech
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具有竞争作用的二维Ising模型及其在$π$-环团簇和阵列及绝热量子计算中的应用

Two-dimensional Ising model with competing interactions and its application to clusters and arrays of $π$-rings and adiabatic quantum computing

A. O'Hare, F. V. Kusmartsev, K. I. Kugel, M. S. Laad

摘要:

我们研究了由包含约瑟夫森$π$结的环($π$环)组成的平面团簇.每一个$π$环都携带一个持续电流,并表现为一个经典的轨道矩。与团簇处的轨道矩的取向相关联的特定状态的类型取决于这些轨道矩之间的相互作用,并且可以容易地控制,即通过偏置电流或通过其他手段。我们发现,这些系统可以描述的二维伊辛模型与竞争最近邻和对角相互作用,并调查该模型的相图。该模型的特点进行了分析的基础上的精确解的小集群,如一个5-网站的正方形plaquette以及平均场型方法的无限正方形晶格的伊辛自旋。计算结果与100 $\times$ 100正方晶格的Monte Carlo模拟结果和实验结果进行了比较。研究表明,$π$环团簇有可能作为一种新型的超导存储元件。所得结果可在实验中得到验证,并适用于在耦合常数缓慢变化的情况下实现态的动态切换的绝热量子计算。

英文摘要:

We study planar clusters consisting of loops including a Josephson $π$-junction ($π$-rings). Each $π$-ring carries a persistent current and behaves as a classical orbital moment. The type of particular state associated with the orientation of orbital moments at the cluster depends on the interaction between these orbital moments and can be easily controlled, i.e. by a bias current or by other means. We show that these systems can be described by the two-dimensional Ising model with competing nearest-neighbor and diagonal interactions and investigate the phase diagram of this model. The characteristic features of the model are analyzed based on the exact solutions for small clusters such as a 5-site square plaquette as well as on a mean-field type approach for the infinite square lattice of Ising spins. The results are compared with spin patterns obtained by Monte Carlo simulations for the 100 $\times$ 100 square lattice and with experiment. We show that the $π$-ring clusters may be used as a new type of superconducting memory elements. The obtained results may be verified in experiments and are applicable to adiabatic quantum computing where the states are switched adiabatically with the slow change of coupling constants.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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