Symmetry-resolved Page curves
- URL: http://arxiv.org/abs/2206.05083v1
- Date: Fri, 10 Jun 2022 13:22:14 GMT
- Title: Symmetry-resolved Page curves
- Authors: Sara Murciano, Pasquale Calabrese and Lorenzo Piroli
- Abstract summary: We study a natural extension in the presence of a conservation law and introduce the symmetry-resolved Page curves.
We derive explicit analytic formulae for two important statistical ensembles with a $U(1)$-symmetry.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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 formulae 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 sub-leading finite-size
corrections.
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