We show that there is an emergent lattice description for the continuous fractional quantum Hall (FQH) systems, with a generalized set of few-body coherent states. In particular, model Hamiltonians of the FQH effect (FQHE) are equivalent to the real-space von Neumann lattice of local projection operators imposed on a continuous system in the thermodynamic limit. It can be analytically derived that tuning local one-body potentials in such lattices amounts to the tuning of individual two- or few-body pseudopotentials. For some cases, we can realize pure few-body pseudopotentials important for stabilizing exotic non-Abelian topological phases. Thus, this new approach can potentially lead to the experimental realization of coveted non-Abelian quantum fluids including the Moore-Read state and the Fibonacci state. The reformulation of the FQHE as a sum of local projections opens up new paths for rigorously proving the incompressibility of microscopic Hamiltonians in the thermodynamic limit.

中文翻译：

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无挫折哈密顿量的分数量子霍尔效应

我们表明，对于连续分数阶量子霍尔（FQH）系统，存在一个具有广义的少体相干态集合的晶格描述。特别是，FQH效应的模型哈密顿量（FQHE）等同于在热力学极限中施加在连续系统上的局部投影算符的实空间冯·诺伊曼格。可以通过分析得出，在这种晶格中调整局部一体电势等于对单个两体或几体伪电势的调整。在某些情况下，我们可以实现对稳定外来的非阿贝尔拓扑相非常重要的纯少体伪势。因此，这种新方法有可能导致梦co以求的非阿贝尔量子流体的实验实现，其中包括摩尔读取态和斐波那契态。