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Local Integrals of Motion in Quasiperiodic Many-Body Localized Systems
by S. J. Thomson, M. Schiró
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Submission summary
| Authors (as registered SciPost users): | Steven Thomson |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202110_00017v1 (pdf) |
| Date submitted: | 2021-10-12 14:49 |
| Submitted by: | Thomson, Steven |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
Local integrals of motion play a central role in the understanding of many-body localization in many-body quantum systems in one dimension subject to a random external potential, but the question of how these local integrals of motion change in a deterministic quasiperiodic potential is one that has received significantly less attention. Here we develop a powerful new implementation of the continuous unitary transform formalism and use this method to directly compute both the effective Hamiltonian and the local integrals of motion for many-body quantum systems subject to a quasiperiodic potential. We show that the effective interactions between local integrals of motion retain a strong fingerprint of the underlying quasiperiodic potential, exhibiting sharp features at distances associated with the incommensurate wavelength used to generate the potential. Furthermore, the local integrals of motion themselves may be expressed in terms of an operator expansion which allows us to estimate the critical strength of quasiperiodic potential required to lead to a localization/delocalization transition, by means of a finite size scaling analysis.
Current status:
Reports on this Submission
Anonymous Report 1 on 2021-11-10 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202110_00017v1, delivered 2021-11-10, doi: 10.21468/SciPost.Report.3827
Strengths
1-Method explained very well
2- Potentially useful method for computing LIOMs beyond 1D
Weaknesses
1- Unclear how groundbreaking result is
2- The authors treat only one-dimensional models, but higher dimensions would be more interesting
Report
The authors study construct the local integrals of motions of an interacting Aubry-Andre-Harper model by developing a new form of tensor flow equations that allows for parallelization.
I find the paper interesting. It is well written. My main issue is whether it reaches the acceptance criteria of SciPost Physics.
What is the main breakthrough wrt to the previous work of the authors, in particular [41,42]? Is it the parallelization algorithm?
Compared to previous approaches with flow equations (in particular [41] by the authors), they now allow for an off-diagonal interaction term (:c^\dagger_i c_j c^\dagger_k c_q:) in the flow equations. In Fig. 11. they show the change with this term included, which is good. But maybe more terms are needed to get the correct LIOMs. How close are the LIOMs constructed to the real ones? It remains unclear to me. Can an estimate be made by e.g. taking the commutator with the original Hamiltonian?
This presents potentially a very useful numerical technique, but it remains unclear how useful it is.
The main advantage of the flow equation approaches over matrix product state based methods seems to be the ability to treat systems in higher than one dimension, but the authors do not do this.
Requested changes
1- Compare and contrast to previous work better in particular [41]
2- Explain limitations of the flow ansatz -e.g. is convergence guaranteed with the ansatz given?
3- Provide clear physically highly significant (breakthrough) advantage over previous methods
4-Demonstrate error of the constructed LIOMs
5- (optional) study model beyond 1D
Minor:
a - What is the point of the normal ordering in the Hamiltonian in (1)? Can one not just write the normal ordered form to begin with?