Universal entanglement of typical states in constrained systems*

We develop a formalism to exactly evaluate the bipartite entanglement of random states in large Hilbert spaces with local and global constraints. We solve the simplest class of constraints which includes the much studied Rydberg-blockaded/Fibonacci chain. The resulting entanglement spectra may be classified into `phases’ depending on their singularities. Our results predict the entanglement of infinite temperature eigenstates in thermalizing constrained systems and provide a baseline for numerical studies.