Ginzburg-Landau Theory for Non-Invertible Symmetry-Breaking Transitions

Abstract:Recently, a generalized Landau paradigm has been proposed, in which a broad class of "unconventional" phase transitions lying beyond the original symmetry-breaking framework of Landau are understood as the symmetry-breaking transitions of generalized symmetries. In particular, in (1+1)D, such "topological" or "deconfined" transitions can be mapped to the symmetry-breaking transitions of non-invertible symmetries. How to extract the universal dynamical properties of the transitions from this understanding? In this paper, we follow the Ginzburg-Landau philosophy and develop a field-theoretic description of such critical points in terms of the fluctuations of local order parameters, now of non-invertible symmetries. The Symmetry Topological Field Theory formalism plays a central role in our analysis, allowing us to identify the algebra of local order parameters from the Lagrangian algebra of a (2+1)D topological order. We illustrate the key ideas and the full steps of this generalized Ginzburg-Landau procedure using the transitions between gapped phases with a simple non-invertible symmetry --- the Rep($S_3$) symmetry.

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

arXiv:2609.06751 [cond-mat.str-el]

(or arXiv:2609.06751v1 [cond-mat.str-el] for this version)

https://doi.org/10.48550/arXiv.2609.06751 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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