Towards topological fixed-point models beyond gappable boundaries
- URL: http://arxiv.org/abs/2111.14868v4
- Date: Sun, 11 Sep 2022 19:50:12 GMT
- Title: Towards topological fixed-point models beyond gappable boundaries
- Authors: Andreas Bauer, Jens Eisert, Carolin Wille
- Abstract summary: We consider fixed-point models for topological phases of matter formulated as discrete path integrals in the language of tensor networks.
All of the established ansatzes for fixed-point models imply the existence of a gapped boundary as well as a commuting-projector Hamiltonian.
We present a more general fixed-point ansatz not affected by the aforementioned restrictions.
- Score: 2.025761610861237
- License: http://creativecommons.org/licenses/by/4.0/
- 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 work, 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.
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