2D and 3D Topological Orders: Universal Wave Function Overlap and String Statistics
summary
The method computes universal wave function overlap directly from ground-state overlaps to extract the S and T matrices as volume-independent constants, distinguishing 2D topological orders and extending to 3D. Tensor networks with an internal gauge symmetry generate the locally indistinguishable degenerate ground states and automatically remove nonuniversal volume factors. Dimension reduction (3D→2D dimension reduction) maps 3D string excitations to 2D particle data, illustrated by loop-gas examples and an S3 gauge-theory case.
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chapters (12)
- 0:00Intro
- 0:36Symm. breaking phases and topologically ordered phases
- 3:11Long-range entanglement and topological order
- 5:18A quantitative description of long-range entanglement
- 10:11Probe/ define topological order via topological invariants
- 20:31Measure topo. order: Universal wavefunction overlap
- 32:12How to generate degenerate ground states
- 42:44Degenerate ground states in tensor network approach
- 45:31Projective representations of 2D/3D mapping class group
- 47:30Topo. properties of excitations and representations of MCG
- 54:41Topo. properties of 3D topo. order from rep. of SL(3, Z)
- 59:363D string-string fusion
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