Universität zu Köln

Bauer, Andreas, Eisert, Jens ORCID: 0000-0003-3033-1292 and Wille, Carolin (2022). A unified diagrammatic approach to topological fixed point models. SciPost Phys. Core, 5 (3). AMSTERDAM: SCIPOST FOUNDATION. ISSN 2666-9366

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Abstract

We introduce a systematic mathematical language for describing fixed point models and apply it to the study to topological phases of matter. The framework is reminiscent of state-sum models and lattice topological quantum field theories, but is formalised and unified in terms of tensor networks. In contrast to existing tensor network ansatzes for the study of ground states of topologically ordered phases, the tensor networks in our formalism represent discrete path integrals in Euclidean space-time. This language is more directly related to the Hamiltonian defining the model than other approaches, via a Trotterization of the respective imaginary time evolution. We introduce our formalism by simple examples, and demonstrate its full power by expressing known families of models in 2+1 dimensions in their most general form, namely string-net models and Kitaev quantum doubles based on weak Hopf algebras. To elucidate the versatility of our formalism, we also show how fermionic phases of matter can be described and provide a framework for topological fixed point models in 3+1 dimensions.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Bauer, Andreas UNSPECIFIED UNSPECIFIED UNSPECIFIED Eisert, Jens UNSPECIFIED orcid.org/0000-0003-3033-1292 UNSPECIFIED Wille, Carolin UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-666784
DOI:	10.21468/SciPostPhysCore.5.3.038
Journal or Publication Title:	SciPost Phys. Core
Volume:	5
Number:	3
Date:	2022
Publisher:	SCIPOST FOUNDATION
Place of Publication:	AMSTERDAM
ISSN:	2666-9366
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language ANYONS Multiple languages Physics, Multidisciplinary Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/66678