Duality viewpoint of criticality

Abstract

In this work, we study quantum many-body systems which are self-dual under duality transformation connecting different symmetry protected topological (SPT) phases. We provide a geometric explanation of the criticality of these self-dual models. More precisely, we show a ground state (quasi-)degeneracy under the periodic boundary conditions,i.e., the ingappability of the bulk spectrum. Equivalently, the symmetry group at criticality, including the duality symmetry, has a mixed 't Hooft anomaly. This approach can not only predict the spectrum of the self-dual model with ordinary 0-form symmetry, but also be applied to that with generalized symmetry, such as higher form and subsystem symmetry. As an application, we illustrate our results with several examples in one and two dimensions, which separate two different SPTs.

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• Generating Lattice Non-invertible Symmetries
• Strong-to-weak spontaneous symmetry breaking meets average symmetry-protected topological order
• Boundary conditions and anomalies of conformal field theories in 1+1 dimensions
• Generalized Kramers-Wannier Duality from Bilinear Phase Map
• Self-$G$-ality in 1+1 dimensions
• A New Framework for Quantum Phases in Open Systems: Steady State of Imaginary-Time Lindbladian Evolution