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Bosonic entanglement renormalization circuits from wavelet theory
by Freek Witteveen, Michael Walter
|As Contributors:||Michael Walter · Freek Witteveen|
|Date submitted:||2021-04-29 22:42|
|Submitted by:||Witteveen, Freek|
|Submitted to:||SciPost Physics|
Entanglement renormalization is a unitary real-space renormalization scheme. The corresponding quantum circuits or tensor networks are known as MERA, and they are particularly well-suited to describing quantum systems at criticality. In this work we show how to construct Gaussian bosonic quantum circuits that implement entanglement renormalization for ground states of arbitrary free bosonic chains. The construction is based on wavelet theory, and the dispersion relation of the Hamiltonian is translated into a filter design problem. We give a general algorithm that approximately solves this design problem and prove an approximation result that relates the properties of the filters to the accuracy of the corresponding quantum circuits. Finally, we explain how the continuum limit (a free bosonic quantum field) emerges naturally from the wavelet construction.
Author comments upon resubmission
We believe that their feedback and suggestions have allowed us to improve the quality and exposition of our work.
We reply in detail to each of the reviewer reports with an Author Reply.
List of changes
- Expanded the introduction
- Added an outline of the organization of the paper
- Added numerics of correlation functions
- Significantly expanded sections 5.2 and 5.3 on continuous wavelet functions
- Added an appendix reviewing the fermionic MERA/wavelet correspondence and a comparison with the bosonic case
- Improved the presentation throughout the manuscript.
See the replies to the individual reviewers for more details on these changes.
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