Universität zu Köln

Bauer, A., Eisert, J. and Wille, C. (2022). Towards topological fixed-point models beyond gappable boundaries. Phys. Rev. B, 106 (12). COLLEGE PK: AMER PHYSICAL SOC. ISSN 2469-9969

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Abstract

We consider fixed-point models for topological phases of matter formulated as discrete path integrals in the language of tensor networks. Such zero-correlation length models with an exact notion of topological invariance are known in the mathematical community as state-sum constructions or lattice topological quantum field theories. All of the established ansatzes for fixed-point models imply the existence of a gapped boundary as well as a commuting-projector Hamiltonian. Thus, they fail to capture topological phases without a gapped boundary or commuting-projector Hamiltonian, most notably chiral topological phases in 2 + 1 dimensions. In this paper, we present a more general fixed-point ansatz not affected by the aforementioned restrictions. Thus, our formalism opens up a possible way forward towards a microscopic fixed-point description of chiral phases and we present several strategies that may lead to concrete examples. Furthermore, we argue that our more general ansatz constitutes a universal form of topological fixed-point models, whereas established ansatzes are universal only for fixed-points of phases, which admit topological boundaries.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Bauer, A. UNSPECIFIED UNSPECIFIED UNSPECIFIED Eisert, J. UNSPECIFIED UNSPECIFIED UNSPECIFIED Wille, C. UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-677298
DOI:	10.1103/PhysRevB.106.125143
Journal or Publication Title:	Phys. Rev. B
Volume:	106
Number:	12
Date:	2022
Publisher:	AMER PHYSICAL SOC
Place of Publication:	COLLEGE PK
ISSN:	2469-9969
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language FIELD-THEORY; 3-MANIFOLDS; INVARIANTS; HOMOLOGY Multiple languages Materials Science, Multidisciplinary; Physics, Applied; Physics, Condensed Matter Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/67729