Connecting the tensor-categorical formulation of anyon condensation with operator algebras and entropic order parameters

Abstract:Anyon condensation that describes the transition between topological quantum field theories can be formulated in the language of tensor categories or that of operator algebras. We deploy the formalism of Doplicher-Haag-Roberts bimodules over quasi-local $\mathrm{C}^{*}$-algebras recently developed in [1] to investigate anyon condensation, which is associated with an extension of a certain operator algebra. The connection between notions in the two formulations is thereby made manifest in an intuitive, diagrammatic manner. An entropic order parameter, as the quantum information-theoretic measure characterising a condensation, is naturally defined, and we give a very simple proof of a bound on it.

Strongly Correlated Electrons (cond-mat.str-el); High Energy Physics - Theory (hep-th); Quantum Physics (quant-ph)

arXiv:2608.12157 [cond-mat.str-el]

(or arXiv:2608.12157v2 [cond-mat.str-el] for this version)

https://doi.org/10.48550/arXiv.2608.12157 Focus to learn more arXiv-issued DOI via DataCite

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.