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Bosonic entanglement renormalization circuits from wavelet theory

by Freek Witteveen, Michael Walter

This Submission thread is now published as

Submission summary

As Contributors: Michael Walter · Freek Witteveen
Preprint link: scipost_202104_00033v2
Date accepted: 2021-06-08
Date submitted: 2021-05-20 12:18
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 provide an approximation theory 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.

Published as SciPost Phys. 10, 143 (2021)

Author comments upon resubmission

We would like to thank the reviewers for their positive response, and Reviewer 1 for the suggestions for improvement.

List of changes

We have implemented all improvements suggested by Reviewer 1.
In addition, we have made the following changes:
- Some cosmetic changes in Appendix D and below the informal approximation theorem in Section 4, where we now cross-reference the precise regularization used for the reader's convenience.
- We have made available and refer to the code that constructs the appropriate wavelet filters and generates the figures in our work, so that the numerical results are easily reproducible (Ref. 26).

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