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Bosonic entanglement renormalization circuits from wavelet theory
by Freek Witteveen, Michael Walter
- Published as SciPost Phys. 10, 143 (2021)
|As Contributors:||Michael Walter · Freek Witteveen|
|Date submitted:||2021-05-20 12:18|
|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 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
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).
Submission & Refereeing History
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- Report 3 submitted on 2021-02-02 17:18 by Dr Tagliacozzo
- Report 2 submitted on 2021-01-20 23:51 by Anonymous
- Report 1 submitted on 2020-12-10 20:05 by Anonymous