Symmetry-resolved Page curves

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

Automated summary

This work investigates the average entanglement entropy of symmetry resolved Page curves in the presence of a conservation law. Explicit analytic formulas are derived for two important statistical ensembles with a U(1)-symmetry, Haar-random pure states and random fermionic Gaussian states. Numerical calculations are conducted to test the predictions and discuss the subleading finite-size corrections.