Highly Entangled Stationary States from Strong Symmetries
Abstract
We find that the presence of strong non-Abelian symmetries can lead to highly entangled stationary states even for unital quantum channels. We derive exact expressions for the bipartite logarithmic negativity, Rényi negativities, and operator space entanglement for stationary states restricted to one symmetric subspace, with focus on the trivial subspace. We prove that these apply to open quantum evolutions whose commutants, characterizing all strongly conserved quantities, correspond to either the universal enveloping algebra of a Lie algebra or the Read-Saleur commutants. The latter provides an example of quantum fragmentation, whose dimension is exponentially large in system size. We find a general upper bound for all these quantities given by the logarithm of the dimension of the commutant on the smaller bipartition of the chain. As Abelian examples, we show that strong U(1) symmetries and classical fragmentation lead to separable stationary states in any symmetric subspace. In contrast, for non-Abelian SU(N) symmetries, both logarithmic and Rényi negativities scale logarithmically with system size. Finally, we prove that, while Rényi negativities with n>2 scale logarithmically with system size, the logarithmic negativity (as well as generalized Rényi negativities with n<2) exhibits a volume-law scaling for the Read-Saleur commutants. Our derivations rely on the commutant possessing a Hopf algebra structure in the limit of infinitely large systems and, hence, also apply to finite groups and quantum groups.
Copyright and License
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Acknowledgement
We are grateful to Berislav Buca, Yujie Liu, Sanjay Moudgalya, Sara Murciano, Subhayan Sahu, Thomas Schuster, Robijn Vanhove, Ruben Verresen, Hironobu Yoshida, and Yizhi You for helpful discussions and also to Tarun Grover for making his lecture notes for the Boulder School 2023 available online. P. S. acknowledges support from the Caltech Institute for Quantum Information and Matter, an National Science Foundation (NSF) Physics Frontiers Center (NSF Grant No. PHY-1733907), and the Walter Burke Institute for Theoretical Physics at Caltech. This work was supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program under Grants Agreement No. 851161 and No. 771537, the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy EXC-2111-390814868, TRR 360 (Project-id No. 492547816), FOR 5522 (Project-id No. 499180199), and the Munich Quantum Valley, which is supported by the Bavarian state government with funds from the Hightech Agenda Bayern Plus.
Data Availability
Data analysis and simulation codes are available on Zenodo upon reasonable request [101].
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Additional details
- National Science Foundation
- PHY-1733907
- Walter Burke Institute for Theoretical Physics
- European Research Council
- European Commission
- 851161
- European Commission
- 771537
- Deutsche Forschungsgemeinschaft
- EXC-2111-390814868
- Deutsche Forschungsgemeinschaft
- 492547816
- Deutsche Forschungsgemeinschaft
- 499180199
- Accepted
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2025-01-23
- Caltech groups
- Institute for Quantum Information and Matter, Walter Burke Institute for Theoretical Physics, Division of Physics, Mathematics and Astronomy (PMA)
- Publication Status
- Published