Matrix product operator algebras II: phases of matter for 1D mixed states
The mathematical classification of topological phases of matter is a crucial step toward comprehending and characterizing the properties of quantum materials. In this study, our focus is on investigating phases of matter in one-dimensional open quantum systems. Our goal is to elucidate the emerging...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2024 |
| País: | España |
| Institución: | Consejo Superior de Investigaciones Científicas (CSIC) |
| Repositorio: | DIGITAL.CSIC. Repositorio Institucional del CSIC |
| OAI Identifier: | oai:digital.csic.es:10261/381329 |
| Acceso en línea: | http://hdl.handle.net/10261/381329 https://www.scopus.com/inward/record.uri?eid=2-s2.0-85187898051&doi=10.1007%2fs11005-024-01778-z&partnerID=40&md5=2c8053402f7343513e9ffd73ae517bb6 |
| Access Level: | acceso abierto |
| Palabra clave: | Open quantum systems Quantum phases of matter Renormalization group Tensor networks Topological order |
| Sumario: | The mathematical classification of topological phases of matter is a crucial step toward comprehending and characterizing the properties of quantum materials. In this study, our focus is on investigating phases of matter in one-dimensional open quantum systems. Our goal is to elucidate the emerging phase diagram of one-dimensional tensor network mixed states that act as renormalization fixed points. These operators hold special significance since, as we prove, they manifest as boundary states of two-dimensional topologically ordered states, encompassing all known two-dimensional topological phases. To achieve their classification we begin by constructing families of such states from C*-weak Hopf algebras, which are algebras with fusion categories as their representations, and we present explicit local fine-graining and coarse-graining quantum channels defining the renormalization procedure. Lastly, we prove that a subset of these states, originating from C*-Hopf algebras, are in the trivial phase. © The Author(s), under exclusive licence to Springer Nature B.V. 2024. |
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