Disordered Phases of Matter with Non-Abelian Symmetries: Instabilities and Enlargements

Speaker:​ Ludwig Zweng (Technische Universität München)

Recent works have developed a unifying framework for classifying ground state phases of matter with a wide range of discrete symmetries—both group-like and non-invertible symmetries—via a holographic correspondence between symmetric operators in d dimensions and topological operators in a d+1 dimensional system often known as the SymTO or SymTFT. Its lattice formulation naturally yields fixed-point commuting Hamiltonians that realize these phases in their ground state. In this work, we extend this framework to disordered and non-equilibrium settings by analyzing excited states of the disordered versions of these fixed-point models with non-Abelian group symmetries. Characterizing symmetry breaking patterns in the excited states requires new tools and diagnostic methods, which we develop in the language of bond algebras and their commutants, and which resolve whether the non-commutativity obstructing eigenstate order is local or merely global. We find that the disordered phase structure can differ dramatically from its clean ground state counterpart: distinct clean ground state phases may merge, a single one may split, and orders with no ground state analogue can appear. We illustrate these phenomena by constructing lattice models for S₃, D₈, and S₄, classifying the distinct excited state phases in each case, and showing that the answer depends on the local Hilbert space and not on the symmetry group alone. Finally, we argue that the SymTFTs that capture ground state phases do not fully capture the intricacies of the excited states.