Abstract
Recent advances promote the study of topological systems with additional synthetic dimensions. In this work, we propose a method to realize the four-dimensional (4D) quantum hall effect by using two strongly interacting bosons. The 1D lattice of the Aubry-André-Harper (AAH) model with two hard-core bosons can be mapped to a synthetic 4D space. The energy spectrum of this system is similar to that of one particle evolving in a 2D AAH model mimicking the 4D quantum hall effect. The energy spectrum contains bulk, edge, and corner states, which can be interpreted as the summation of two independent single-particle spectra in the 1D Aubry-André-Harper (AAH) model. Our results pave the way to realizing higher-dimension physics such as topology and localization by using many particles.
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