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arXiv · 2508.17989

Incompressible quantum liquid on the four-dimensional sphere

Junwen Zhao·Xue Meng·Wei Zhu·Congjun Wu
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Abstract

The study of quantum Hall effect (QHE) is a foundation of topological physics, inspiring extensive explorations of its high-dimensional generalizations. Notably, the four dimensional (4D) QHE has been experimentally 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.

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Junwen Zhao, Xue Meng, Wei Zhu, Congjun Wu. 2025-08-25. Incompressible quantum liquid on the four-dimensional sphere. https://doi.org/10.1103/qygs-j2ys

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