标题： 不可压缩的量子液体在四维球面上 显示英文标题

标题： Incompressible quantum liquid on the four-dimensional sphere

摘要： 量子霍尔效应（QHE）的研究是拓扑物理的基础，激发了对其高维推广的广泛探索。 值得注意的是，四维（4D）QHE已经在合成量子系统中被实验实现，包括冷原子、光子晶格和超材料。 然而，4D QHE系统中的多体效应仍然了解甚少。 在本研究中，我们通过构建受Laughlin开创性工作启发的微观波函数来探讨这个问题。 采用广义伪势框架，我们推导出一个由两体投影算符组成的精确微观哈密顿量，该算符使微观波函数消失。 在小尺寸系统上的对角化显示，准-hole态保持零能，而准粒子态表现出有限能隙，这与不可压缩态一致。 此外，计算了配对分布以证实波函数的液态特性。 我们的工作为高维分数拓扑态提供了一个初步的理解。 显示英文摘要

摘要： The study of quantum Hall effect (QHE) is a foundation of topological physics, inspiring extensive explo- rations of its high-dimensional generalizations. Notably, the four-dimensional (4D) QHE has been experi- mentally realized in synthetic quantum systems, including cold atoms, photonic lattices, and metamaterials. However, the many-body effect in the 4D QHE system remains poorly understood. In this study, we explore this problem by formulating the microscopic wavefunctions inspired by Laughlin's seminal work. Employing a generalized pseudo-potential framework, we derive an exact microscopic Hamiltonian consisting of two-body projectors that annihilate the microscopic wavefunctions. Diagonalizations on a small size system show that the quasi-hole states remain zero energy while the quasi-particle states exhibit a finite gap, in consistency with an incompressible state. Furthermore, the pairing distribution is calculated to substantiate the liquid-like nature of the wavefunction. Our work provides a preliminary understanding to the fractional topological states in high dimension.