Matrix Product Operator Algebras II

Autor(en)

Alberto Ruiz de Alarcón, José Garre-Rubio, András Molnár, David Pérez-García

Abstrakt

The classification of topological phases of matter is fundamental to understand and characterize the properties of quantum materials. In this paper we study phases of matter in one-dimensional open quantum systems. We define two mixed states to be in the same phase if both states can be transformed into the other by a shallow circuit of local quantum channels. We aim to understand the phase diagram of matrix product density operators that are renormalization fixed points. These states arise, for example, as boundaries of two-dimensional topologically ordered states. We first construct families of such states based on C*-weak Hopf algebras, the algebras whose representations form a fusion category. More concretely, we provide explicit local fine-graining and local coarse-graining quantum channels for the renormalization procedure of these states. Finally, we prove that those arising from C*-Hopf algebras are in the trivial phase.

Organisation(en)

Institut für Mathematik

Externe Organisation(en)

Universidad Complutense De Madrid

Anzahl der Seiten

31

DOI

https://doi.org/10.48550/arXiv.2204.06295

Publikationsdatum

04-2022

ÖFOS 2012

103019 Mathematische Physik, 103025 Quantenmechanik

Schlagwörter

Link zum Portal

https://ucris.univie.ac.at/portal/de/publications/matrix-product-operator-algebras-ii(326d1c4d-1006-4d96-ac24-8a122687c5ce).html