CMSA Topological Quantum Matter Seminar: Dipolar and modulated symmetry protected topological phases

Modulated symmetries are symmetries whose symmetry generators exhibit spatial modulations. We will discuss one-dimensional symmetry protected topological (SPT) phases protected by modulated symmetries. We will present a simple recipe for constructing modulated SPT models by generalizing the concept of decorated domain walls. We will then focus on the simplest modulated SPT protected by dipolar symmetries, classify them using matrix product states and construct their response field theories using twisted finite tensor gauge theories.