Highlyentangled stationary states from strong symmetries
Abstract
We find that the presence of strong nonAbelian conserved quantities 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 to the ReadSaleur 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 nonAbelian 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 ReadSaleur 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.
 Publication:

arXiv eprints
 Pub Date:
 June 2024
 DOI:
 10.48550/arXiv.2406.08567
 arXiv:
 arXiv:2406.08567
 Bibcode:
 2024arXiv240608567L
 Keywords:

 Quantum Physics;
 Condensed Matter  Strongly Correlated Electrons
 EPrint:
 17 Pages, 7 figures. Comments are welcome