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.

Symmetry-resolved Page curves / Murciano, S.; Calabrese, P.; Piroli, L.. - In: PHYSICAL REVIEW D. - ISSN 2470-0010. - 106:4(2022), pp. 1-13. [10.1103/physrevd.106.046015]

Symmetry-resolved Page curves

Murciano, S.;Calabrese, P.;Piroli, L.
2022-01-01

Abstract

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.
2022
106
4
1
13
046015
https://doi.org/10.1103/PhysRevD.106.046015
https://arxiv.org/abs/2206.05083
Murciano, S.; Calabrese, P.; Piroli, L.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/131446
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