Gauging quantum states with nonanomalous matrix product operator symmetries

Autor(en)

José Garre-Rubio, Ilya Kull

Abstrakt

Gauging a global symmetry of a system amounts to introducing new degrees of freedom whose transformation rule makes the overall system observe a local symmetry. In quantum systems there can be obstructions to gauging a global symmetry. When this happens the symmetry is dubbed anomalous. Such obstructions are related to the fact that the global symmetry cannot be written as a tensor product of local operators. In this paper we study nonlocal symmetries that have an additional structure: They take the form of a matrix product operator (MPO). We exploit the tensor network structure of the MPOs to construct local operators from them, satisfying the same group relations; that is, we are able to localize even anomalous MPOs. For nonanomalous MPOs, we use these local operators to explicitly gauge the MPO symmetry of a one-dimensional quantum state obtaining nontrivial gauged states. We show that our gauging procedure satisfies all the desired properties that the standard on-site case does. We also show how this procedure is naturally represented in matrix product states protected by MPO symmetries. In the case of anomalous MPOs, we shed light on the obstructions to gauging these symmetries.

Organisation(en)

Institut für Mathematik, Quantenoptik, Quantennanophysik und Quanteninformation

Journal

Physical Review B

Band

107

Anzahl der Seiten

12

ISSN

2469-9950

DOI

https://doi.org/10.1103/PhysRevB.107.075137

Publikationsdatum

02-2023

Peer-reviewed

Ja

ÖFOS 2012

103015 Kondensierte Materie, 103029 Statistische Physik

ASJC Scopus Sachgebiete

Electronic, Optical and Magnetic Materials, Condensed Matter Physics

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/6985e3bb-6927-4b21-8af1-afb04f3956d8