Symmetry-resolved Page curves

Given a statistical ensemble of quantum states, the corresponding Page curve quantifies average entanglement entropy associated with each possible spatial bipartition system. In this work, we study natural extension in presence conservation law and introduce symmetry-resolved curves, characterizing bipartite entropies. We derive explicit analytic formulas for two important ensembles $U(1)$-symmetry: Haar-random pure states random fermionic Gaussian states. former case, curves can be obtained an elementary way from knowledge standard one. This is not true result thermodynamic limit based on combination techniques random-matrix large-deviation theories. test our predictions against numerical calculations discuss subleading finite-size corrections.