An Introduction to Symmetry Protected Topological Phases

Sammanfattning: In this thesis, we aim to display characteristics of symmetry protected topological phases within quantum mechanics (QM). Building on well known aspects of QM, we relate the formalism to basic group representation theory, and review the connection between projective symmetries and protected vacuum degeneracies. Symmetries acting projectively on the Hilbert space, corresponding to non-trivial equivalence classes in group cohomology, guarantee degenerate vacua. Furthermore, considering QM in the framework of path integrals, we see that an SPT phase for the system consisting of a particle on a circle maps to a so-called "anomaly theory" in one dimension higher.