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Bosonic entanglement renormalization circuits from wavelet theory

by Freek Witteveen, Michael Walter

Submission summary

As Contributors: Michael Walter · Freek Witteveen
Preprint link: scipost_202104_00033v1
Date submitted: 2021-04-29 22:42
Submitted by: Witteveen, Freek
Submitted to: SciPost Physics
Academic field: Physics
  • Quantum Physics
Approach: Theoretical


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.

Current status:
Editor-in-charge assigned

Author comments upon resubmission

We would like to thank the editor and the reviewers for their thoughtful consideration of our work.
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

We have
- 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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