Analytic Optimization of a MERA network and its Relevance to Quantum Integrability and Wavelet

Understand

I present an example of how to analytically optimize a multiscale entanglement renormalization ansatz for a finite antiferromagnetic Heisenberg chain.

• For this purpose, a quantum-circuit representation is taken into account, and we construct the exactly entangled ground state so that a trivial IR state is modified sequentially by operating separated entangler layers (monodromy operators) at each scale.
• The circuit representation allows us to make a simple understanding of close relationship between the entanglement renormalization and quantum integrability.
• We find that the entangler should match with the $R$-matrix, not a simple unitary, and also find that the optimization leads to the mapping between the Bethe roots and the Daubechies wavelet coefficients.