Exploring ground state phase diagrams of Rydberg atom arrays with finite projected entangled-pair states

Rydberg atom arrays (RAA) have been advocated as a promising avenue for the quantum simulation of different exotic quantum states. Numerical predictions for the ground state properties of this experimental platform can, however, be challenging in two-dimensional setups. In particular, faithfully treating long-range interactions is often crucial for distinguishing the fate of competing phases, but it usually comes at considerable cost. Projected entangled-pair states (PEPS), optimized via a sampling-based approach, have been shown to deal with such terms on the same ground as shorter-range ones. In this work, we employ these tools to investigate debated physical questions in different frustrated geometries of RAA, from the emergence of spin-glass physics on the Kagomé lattice to topological order beyond the PXP model on the Ruby lattice. By that, we contribute to establishing PEPS as well-suited tools for creating digital twins of RAA experiments.