Topological Goldstone phases of matter

Abstract

We consider the possibility for phases of matter in which a continuous symmetry is spontaneously broken in a \emph{topologically non-trivial} way, which, roughly, means that the action for the Goldstone modes contains a quantized topological term, and could manifest in, for example, non-trivial quantum numbers of topological defects of the order parameter. We show that, in fact, such a scenario can occur only when the system is in a non-trivial symmetry-protected topological (SPT) or symmetry-enriched topological (SET) phase with respect to the residual symmetry; or alternatively, if the original symmetry before spontaneous symmetry breaking acts on the system in an "anomalous" way. Our arguments are based on a general correspondence between topological defects of the order parameter and topological defects of a background gauge field for the residual symmetry.

arXiv comment4 pages + 1 page appendix. v3 Published version, with some additional physical explanations

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• Higher Berry Curvature from the Wave Function I: Schmidt Decomposition and Matrix Product States
• Higher Berry Curvature from the Wave function II: Locally Parameterized States Beyond One Dimension
• Charting the space of ground states with tensor networks
• Topological Kondo effect with spinful Majorana fermions
• Anomalous continuous symmetries and quantum topology of Goldstone modes
• Theory of topological defects and textures in two-dimensional quantum orders with spontaneous symmetry breaking
• Nonlinear Lifshitz Photon Theory in Condensed Matter Systems
• Quantum Restored Symmetry Protected Topological Phases
• Crystallography, Group Cohomology, and Lieb-Schultz-Mattis Constraints