Classification of 2D Gapped Ground States With Strict Area Law
summary
Assuming a strict area law on every constant-size disk, any 2D gapped ground state on a disk is mapped by a constant‑depth quantum circuit (built by local Petz recovery maps and Stinespring dilations) into the ground space of a local commuting projector model — the generalized string‑net specified by a unitary fusion category. The proof uses quantum Markov chains and information convex sets, implements hole‑punching depth‑one channels, and yields consequences for classifying phases and NP‑style witnesses for 2D commuting Hamiltonians.
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chapters (17)
- 0:002D gapped ground states
- 1:08Area law in 1D systems
- 3:15Higher dimensions challenges
- 5:26Strict area law assumption
- 7:58Generalized string net models
- 10:51Unitary fusion categories
- 13:21Commuting Hamiltonians complexity
- 17:01Quantum phase classification
- 20:24Quantum Markov chains
- 23:58Entanglement bootstrap
- 28:18String net Hilbert space
- 31:06Local circuits hole punching
- 35:05Information convex sets
- 40:51Convex sets structure theorem
- 43:06Deriving vertex constraints
- 47:25Ground energy applications
- 48:30Summary and future
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