2026-06-29T07:49:51Zhttps://docta.ucm.es/rest/oai/request

oai:docta.ucm.es:20.500.14352/652752023-08-28T17:54:46Zcom_20.500.14352_14col_20.500.14352_15

Matrix product operator algebras II: phases of matter for 1D mixed states Ruiz de Alarcón, Alberto Garre Rubio, Jose Molnár, Andras Pérez García, David 51-73 530.1 Mathematical Physics Quantum Physics Strongly Correlated Electrons Física matemática Matemáticas (Matemáticas) Análisis matemático 12 Matemáticas 1202 Análisis y Análisis Funcional 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. Unión Europea. Horizonte 2020 Ministerio de Ciencia e Innovación (MICINN) Centro de Excelencia Severo Ochoa Comunidad de Madrid Depto. de Análisis Matemático y Matemática Aplicada Fac. de Ciencias Matemáticas FALSE unpub 2023-06-21T02:18:10Z 2023-06-21T02:18:10Z journal article https://hdl.handle.net/20.500.14352/65275 XXXX-XXXX eng GAPS (648913) MCIN/AEI/- 10.13039/501100011033 (PID2020-113523GB-I00 and grant BES-2017-081301 CEX2019- 000904-S; SEV-2015-0554 QUITEMAD-CM (P2018/TCS-4342). open access application/pdf