论文标题
部分可观测时空混沌系统的无模型预测
Constraints of kinematic bosonization in two and higher dimensions
论文作者
论文摘要
与共同的智慧相反，菲尔米金系统的局部隆体化存在于更高的维度。有趣的是，由此产生的骨变量必须满足量规类型的局部约束。他们有效地取代了长途交换互动。在这项工作中，我们详细研究了很久以前提出的这种系统的属性。特别是，进一步阐述了约束对晶格几何和速度多重性的依赖性，现在已针对具有任意大小的所有二维矩形晶格进行了分类。对于少数小型系统，可以通过分析求解约束，并显示出减少自旋汉密尔顿的完整光谱与原始的费米子量一致。等效性扩展到外部Wegner $ Z_2 $字段中的费米子。还通过针对Wegner变量的特定配置进行明确计算来说明它。最后，讨论了与最近提出的二元性网络的可能联系。
Contrary to the common wisdom, local bosonizations of fermionic systems exist in higher dimensions. Interestingly, resulting bosonic variables must satisfy local constraints of a gauge type. They effectively replace long distance exchange interactions. In this work we study in detail the properties of such a system which was proposed a long time ago. In particular, dependence of the constraints on lattice geometry and fermion multiplicity is further elaborated and is now classified for all two dimensional, rectangular lattices with arbitrary sizes. For few small systems the constraints are solved analytically and the complete spectra of reduced spin hamiltonias are shown to agree with the original fermionic ones. The equivalence is extended to fermions in an external Wegner $Z_2$ field. It is also illustrated by an explicit calculation for a particular configuration of Wegner variables. Finally, a possible connection with the recently proposed web of dualities is discussed.
