TL;DR
This paper reformulates the Algebraic Bethe Ansatz for spin chains using tensor networks, revealing new structural insights and potential extensions to higher dimensions.
Contribution
It introduces a tensor network representation of Bethe eigenstates, bridging algebraic methods with tensor network techniques and suggesting extensions to two-dimensional systems.
Findings
Bethe eigenstates can be expressed as Matrix Product States
Tensor network formulation preserves spin conservation
Potential for extending Bethe Ansatz to 2D systems
Abstract
We describe the Algebraic Bethe Ansatz for the spin-1/2 XXX and XXZ Heisenberg chains with open and periodic boundary conditions in terms of tensor networks. These Bethe eigenstates have the structure of Matrix Product States with a conserved number of down-spins. The tensor network formulation suggestes possible extensions of the Algebraic Bethe Ansatz to two dimensions.
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Videos
The Algebraic Bethe Ansatz and Tensor Networks· youtube
