Symmetry and Topological Order in Quantum States
summary
Shows a practical recipe: use matrix product states in canonical form, build a generalized transfer matrix by inserting the on-site symmetry, and take its dominant eigenvector to read off the projective representation acting on Schmidt (edge) degrees of freedom. That invariant (commutators ±1, traces like Tr[u u]=±1) labels 1D SPT phases such as the Haldane/AKLT example, works directly with DMRG/MPS outputs, warns about false results near long correlation lengths, and extends to minimally entangled states* on cylinders for symmetry-enriched topological order.
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chapters (13)
- 0:00Introduction
- 2:03SBMT phases in onedimensional systems
- 9:37Open chain
- 11:45Symmetry protected topological phases
- 14:35Projective representations
- 21:07Nonlocal order
- 25:39Critical state
- 26:30Matrix product states
- 35:20Time reversing symmetry
- 42:20Why do we get finite
- 47:43The enriched topological order
- 53:43Topological degeneracy
- 58:43Honeycomb lattice
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