Entanglement in Many Body Quantum Systems
summary
Describes concrete examples and results: the quantum dimer / resonating valence bond construction gives an equal‑weight ground state at the Rokhsar–Kivelson point that on a frustrated (triangular) lattice yields fourfold degeneracy whose ground states are locally indistinguishable. Uses PEPS/tensor‑network constructions and finite‑group symmetries to build topological sectors, and applies Lieb–Robinson bounds to prove creating such order with geometrically local dynamics needs time ~ system size. Known 2D models are gapped and stable under local perturbations; 3D cases are subtler.
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chapters (14)
- 0:00Intro
- 0:56SETUP
- 3:37Outlook
- 9:04Phases. Order. Symmetries
- 16:11BO's. New type of order. Topological order. RVB. QDM
- 19:54Quantum Dimer Model
- 27:39Topological order in the QDM
- 37:29Definition of topological order
- 45:12Consequences of topological order
- 48:27Topological order is difficult to create
- 57:04Basics in PEPS. Box-leg notation for tensors
- 58:031D PEPS = MPS
- 58:49Parent Hamiltonian
- 59:12Topology in PEPS. Gauge symmetry
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