Скачать или смотреть HEP-TN Seminar: Andreas Bauer "A unified diagrammatic approach to topological fixed point models"

In this talk, Andreas Bauer (Freie Universität Berlin) introduces a systematic mathematical language for describing fixed point models and applies 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 this 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. Andreas illustrates the formalism at hand of simple examples, and demonstrates 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, Andreas also shows how fermionic phases of matter can be described and provide a framework for topological fixed point models in 3+1 dimensions.



This seminar is part of an online series on Tensor Networks in High Energy Physics (HEP-TN). For more details, and schedule of upcoming talks, visit: www.heptnseminar.org.


This talk was recorded on February 11, 2020 at the Albert Einstein Institute in Potsdam-Golm.