Topological Order in Projected Entangled Pair States

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Local tensors with a finite-group G-injective PEPS structure generate both a parent Hamiltonian and its ground states; a hidden virtual symmetry strings on the auxiliary legs label the torus ground-state sectors, make pointlike excitations into string endpoints, and give anyonic counting via group conjugacy/irreps. Overlaps and correlations follow from the cylinder transfer operator which blocks by symmetry sectors; adding string tension (lambda) maps the transfer spectrum to an Ising transition and shows how distinct finite-volume ground states collapse or remain orthogonal in the thermodynamic limit.

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" chapters (15)

1. 0:00Introduction
2. 3:20Model
3. 9:22Topological Order
4. 14:20Ground States
5. 22:05Hidden Symmetry
6. 30:55Injectivity Property
7. 32:02Parameterization
8. 33:25Moving strings
9. 36:44Discrete symmetry
10. 39:30Degenerate symmetry
11. 41:02Excitations
12. 43:04Normalization transformations
13. 44:55String tension
14. 48:05Transfer operator
15. 55:40Phase transition