SciPost Physics Core

SciPost Phys. Core 5, 038 (2022) · published 25 July 2022

• doi: 10.21468/SciPostPhysCore.5.3.038
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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 established is reminiscent to that of state-sum models and lattice topological quantum field theories, but is formalized 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 directly represent discrete path integrals in Euclidean space-time. This language is more immediately related to the Hamiltonian defining the model than other approaches, via a Trotterization of the respective imaginary time evolution. We illustrate our formalism at hand of 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.

• Bauer, Disentangling modular Walker-Wang models via fermionic invertible boundaries
  Phys. Rev. B 107, 085134 (2023) [Crossref]
• Bauer, Topological error correcting processes from fixed-point path integrals
  Quantum 8, 1288 1288 (2024) [Crossref]
• Magdalena de la Fuente et al., Bulk-to-boundary anyon fusion from microscopic models
  64, 111904 (2023) [Crossref]
• Bauer et al., Towards topological fixed-point models beyond gappable boundaries
  Phys. Rev. B 106, 125143 (2022) [Crossref]