Tensor Networks and Conformal Field Theory

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Constructs lattice spin wavefunctions as correlators of CFT vertex operators (chiral boson with charge α) and uses null‑vector decoupling to derive parent Hamiltonians and linear equations for correlators; variationally tunes α to approximate the XXZ chain across Δ∈(−1,1) and recovers c=1 from Rényi‑2 entropy scaling, with exact matches at special points including the inverse‑square Haldane–Shastry limit; extends to SU(2)k (spin‑1 from k=2 gives c=3/2) and builds 2D spin‑liquid parents that truncate to local terms with ~96–99% overlap on ~20 sites. CFT correlators as wavefunctions null‑vector parent Hamiltonians

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" chapters (14)

1. 0:00Introduction to networks
2. 4:17Network construction basics
3. 7:15Infinite dimensional networks
4. 11:25Applications and symmetry
5. 13:22Simple conformal theory
6. 18:04Variational method application
7. 23:11Numerical verification
8. 29:08Internal symmetries
9. 33:55Rational conformal theory
10. 38:40Spin chain models
11. 45:01Hamiltonian construction
12. 51:29Generalizations and limits
13. 56:46Spin liquid properties
14. 59:37Conclusion and Q&A