Abstract
The topologically ordered phases, discussed in the last chapter, are the fundamental zero-temperature phases—if you allow for arbitrary changes of your system (i.e., the Hamiltonian), you can continuously interpolate between all other phases. But this is a too restrictive view and would make us miss important phase differences, as between solids and liquids. In many situations there are symmetries that all physically realizable perturbations, at least on long length scales, uphold. In those situations it is natural to consider what the possible phases are if we restrict ourselves to systems with a certain symmetry, i.e., symmetry protected phases.
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Notes
- 1.
A gap to all states is actually not needed. To be more precise, we need a gap to all exitations that can transport current. In a real quantum Hall system there is generically both charged excitations that are local and gapless excitations that cannot transport charge.
- 2.
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Klein Kvorning, T. (2018). Response Theory and Symmetry Protected Topological Phases. In: Topological Quantum Matter. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-96764-6_3
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