Motivated by recent success of the Lee-Huang-Yang (LHY) quantum correction on dipolar condensates, I numerically studied a fast rotating quasi-two-dimensional Rydberg-dressed Bose-Einstein condensate (BEC) where LHY correction has been taken into account. In a rotating Rydberg-dressed BEC of reduced dimensionality, I show that there is room to tune the LHY coupling against the long- and short-range interactions. The competition between the LHY coupling and the long-/short-range interaction then results in rich phase diagrams for the vortex lattice structures. Most of results can be deemed in the context of superfluid (SF)-supersolid (SS) transition. In particular, I propose that trapping effect of the SS triangles or grids can lead to the clustering of multiple vortices. I have provided a way to estimate the number of vortices clustered in the SS lattice.

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