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arXiv · 1608.02205

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

Hiroaki Matsueda
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Abstract

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.

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Hiroaki Matsueda. 2016-08-07. Analytic Optimization of a MERA network and its Relevance to Quantum Integrability and Wavelet. https://arxiv.org/abs/1608.02205

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