RT Journal Article
T1 Matrix product operator algebras II: phases of matter for 1D mixed states
A1 Ruiz de Alarcón, Alberto
A1 Garre Rubio, Jose
A1 Molnár, Andras
A1 Pérez García, David
AB 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.
LK https://hdl.handle.net/20.500.14352/65275
UL https://hdl.handle.net/20.500.14352/65275
LA eng
NO Unión Europea. Horizonte 2020
NO Ministerio de Ciencia e Innovación (MICINN)
NO Centro de Excelencia Severo Ochoa
NO Comunidad de Madrid
DS Docta Complutense
RD 19 dic 2025