# Topological phases and their transitions in 1D

### APA

Verresen, R. (2016). Topological phases and their transitions in 1D. Perimeter Institute. https://pirsa.org/16080031

### MLA

Verresen, Ruben. Topological phases and their transitions in 1D. Perimeter Institute, Aug. 02, 2016, https://pirsa.org/16080031

### BibTex

@misc{ pirsa_PIRSA:16080031, doi = {10.48660/16080031}, url = {https://pirsa.org/16080031}, author = {Verresen, Ruben}, keywords = {Condensed Matter}, language = {en}, title = {Topological phases and their transitions in 1D}, publisher = {Perimeter Institute}, year = {2016}, month = {aug}, note = {PIRSA:16080031 see, \url{https://pirsa.org}} }

Ruben Verresen Harvard University

**Collection**

**Talk Type**Scientific Series

**Subject**

## Abstract

One dimensional symmetry protected topological (SPT) phases are gapped phases of matter whose edges are degenerate if the Hamiltonian respects a particular symmetry. With their interacting classification having been understood since 2010, we would like to further our understanding by addressing the following two questions: (1) Is there a unified way of understanding some of the exactly soluble models for 1D SPTs? And (2) if we are given two arbitrary SPTs, can we predict the structure of the phase transition between them? The answers turn out to be surprisingly simple. The first is given by relating various models to the Kitaev chain, uncovering new facts about some well-known SPTs. As for the transition between two arbitrary SPTs, it is generically described by a free conformal field theory which is determined by the topological class of the gapped phases.