Symmetry-resolved Page curves

Murciano, Sara; Calabrese, Pasquale; Piroli, Lorenzo

doi:10.1103/PhysRevD.106.046015

Symmetry-resolved Page curves

Sara Murciano
(
- INFN, Trieste
)
,
Pasquale Calabrese
(
- INFN, Trieste and
- ICTP, Trieste
)
,
Lorenzo Piroli
(
- ENS, Paris, IPM
)

Jun 10, 2022

13 pages

Published in:

Phys.Rev.D 106 (2022) 4, 046015

Published: Aug 15, 2022

e-Print:

2206.05083 [hep-th]

DOI:

10.1103/PhysRevD.106.046015 (publication)

View in:

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Abstract: (APS)

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.

Note:

13 pages, 4 Figures

entropy: entanglement
matrix model: random
correction: finite size
statistical
U(1)
numerical calculations
thermodynamical
conservation law

References(141)

Figures(2)

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