'Gauging' Time Reversal Symmetry in Tensor Network States
summary
Proposes a concrete procedure to “gauge” time reversal in tensor network states by defining a local complex conjugation on tensors and implementing symmetry twists by inserting operators on the virtual indices (analogue of flux threading). Shows in 1D MPS the composition rule gives a projective sign (M* M = ±1) that detects SPT order (AKLT gives −1), extends to 2D Z2×T examples where Z2 fluxes carry T^2=−1, and flags gaps: works for gapped wavefunctions but not yet for Hamiltonians or beyond‑cohomology 3D.
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chapters (15)
- 0:00Intro
- 1:58What is gauging?
- 3:17What is time reversal?
- 5:44Gauging time reversal?
- 12:55Why gauge time reversal?
- 17:10How to gauge time reversal?
- 17:44Gauging (1) in more detail
- 24:37Time Reversal - Anti-unitary!
- 26:54Hint: product state
- 27:54Solution: Tensor Product Representation
- 31:05Adding a symmetry twist
- 43:22Adding a time reversal twist
- 45:371D Time Reversal Symmetry Protected Topological Order
- 55:08Summary
- 55:38Open questions
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