The Algebraic Bethe Ansatz and Tensor Networks

on YouTube ↗01h 02m

" summary

Constructs exact eigenstates of the XXZ/XXX spin chain by writing the Bethe wavefunction as a product of commuting B-operators rather than an N! coordinate sum, gives explicit L-operator and R-matrix formulas, derives Bethe equations and energy via logarithmic derivative, defines the quantum determinant and K-matrices for open boundary reflection algebra, and builds a tensor network representation (periodic and doubled open-chain versions) that reproduces the coordinate Bethe wavefunction and claims improved computational efficiency for simulations in optical-lattice setups.

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" chapters (8)

1. 0:00Bethe Ansatz and spin models
2. 10:53Bethe wave functions to tensor networks
3. 22:59Young-Baxter equation
4. 32:22Commutation relations
5. 44:03Spin chain experiments
6. 48:39Open boundary conditions
7. 58:03Tensor networks for open BCs
8. 1:00:54Spectral equations

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