Condensed Matter Theory Forum - What we can learn from unwinding SPT phases

Symmetry protected topological (SPT) phases are arguably the simplest non-trivial gapped phases of matter and are characterized by protected boundary modes and a 'topological' response to gauge fields. The program of systematically classifying SPT phases has provided important insights into the many ways symmetries are 'anomalously' manifested in quantum many-body systems and the constraints imposed on their dynamics. Using examples of lattice and continuum toy models, I will show how these insights can be arrived at by attempting to 'unwind' a non-trivial SPT phase to a trivial one. I will also describe how, more recently, this has been used to demonstrate the existence of novel gapless states of matter and exotic phase diagrams.