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Decoherence and pointer states in small antiferromagnets: A benchmark test
by H. C. Donker, H. De Raedt, M. I. Katsnelson
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Submission summary
| Authors (as registered SciPost users): | Hylke Donker |
| Submission information | |
|---|---|
| Preprint Link: | http://arxiv.org/abs/1612.03099v1 (pdf) |
| Date submitted: | 2016-12-12 01:00 |
| Submitted by: | Donker, Hylke |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Computational |
Abstract
We study the decoherence process of a four spin-1/2 antiferromagnet that is coupled to an environment of spin-1/2 particles. The preferred basis of the antiferromagnet is discussed in two limiting cases and we identify two $\it{exact}$ pointer states. Decoherence $\it{near}$ the two limits is examined whereby entropy is used to quantify the $\it{robustness}$ of states against environmental coupling. We find that close to the quantum measurement limit, the self-Hamiltonian of the system of interest can become dynamically relevant on macroscopic timescales. We illustrate this point by explicitly constructing a state that is more robust than (generic) states diagonal in the system-environment interaction Hamiltonian.
Current status:
Reports on this Submission
Report #2 by Anonymous (Referee 2) on 2017-1-4 (Invited Report)
- Cite as: Anonymous, Report on arXiv:1612.03099v1, delivered 2017-01-04, doi: 10.21468/SciPost.Report.60
Strengths
1) Numerical analysis of a very important problem, the determination of the pointer states.
2) The analysis of the strong coupling limit suggests non-trivial effects
Weaknesses
1) The analysis is restricted to few cases a discussion on how to draw general statements from the simulations is limited
2) The presentation can be considerably improved
Report
The paper by Donker et al deals with a very important problem, the identification of the pointer states for a quantum system coupled to an external bath. Through a numerical integration of the equation of motion they face the question, both in the strong and weak coupling limit, on how to identify the pointer states. As already said, the question is important and the paper hints at clarifying some interesting aspects of the issue.
The model analysed by the authors consists of a four-site antiferromagnetic coupled through a z-z coupling to a spin bath. Both the system-bath and the intra-bath couplings are random in magnitude. Because of numerical limitations (as far as I understand) the analysis is limited to few initial configurations.
Starting from the two extreme limits in the strong and weak coupling regimes the authors develops the numerics around those showing that some non-trivial effects appears. Personally I found the results in the strong coupling regime of particular interest.
Despite this positive judgment I find that there are several other aspects of the paper that need to be improved. If not in additional simulations, I think that a revised presentation will certainly help. I will list below the points where the paper would benefit from some additional discussion
- I am slightly confused from the introduction of the choice of the initial states. If on one side I see the reason for this choice, on the other side it seems implied that there are sizeable non-Markovian effects. It seems to me that the different degree on this "non-Markovian behaviour" and its differences going from the weak to the strong coupling are not addressed. I guess a discussion of this point is relevant for the analysis (or at least the authors should point out why/if it is not relevant)
- I was unable to find in the paper more informations on the choice of the random couplings. It seemed in reading that a single choice of the couplings was presented
- I miss to see the reason of choosing 4-sites for the system instead of 2 (for example). Is there something that we learn from this choice?
- The presentation may also improve considerably in the introduction and definition of various quantities. For example: the reduced density matrix \rho is introduced in page 2 and defined in page 5, similarly for the Hamiltonian H
- I think that the discussion on how to draw some general conclusions from the analysis of few cases can be improved.
- The format of Fig 2 and 4 should be improved, some features discussed in the text are difficult to visualise.
Requested changes
These are listed in the report
Report #1 by Anonymous (Referee 1) on 2016-12-29 (Invited Report)
- Cite as: Anonymous, Report on arXiv:1612.03099v1, delivered 2016-12-29, doi: 10.21468/SciPost.Report.58
Strengths
-The authors address here a rather fundamental issue: namely finding the pointer states, the most immune states with respect to environmental decoherence, of an interacting system, here a small collection of coupled spin ½.
- The results look sound and reliable.
- The main result of the paper concerns the strong system-environemnt regime. The author show explicitly that contrary to the naive expectation, some stateswhich are not diagonal in the interaction Hamiltonian $H_I$ can become more stable with time than typical states that are diagonal in $H_I$.
Weaknesses
- The authors studies only very small systems (4 spins 1/2 for the system coupled to 16 spins 1/2 for the environment). The system is far from an experimentally realistic system as studied in [42].
- The emergence of classicality cannot be seriously studied with such small systems.
- As such, this study is more of an exercise to illustrate that point states should not be chosen with care especially in the strong coupling case.
- Figures'caption should be more self-contained. We are always obliged to dig in the text the values of the chosen parameters.
Report
I am somewhat mixed by this paper. As I wrote above, this is more of a simple numerical exercise to look at the dynamics of a very small Heisenberg AF system (4 spins) coupled to a small environment of 16 spin 1/2. In that sense, this is not very original nor very conclusive for more realistic systems.
However, this study has the merit to simply illustrate that pointer states are not always the most intuitive ones particularly in the strong system-environment coupling where one would think at first sight that states diagonal in $H_I$ would be appropriate pointer states.
Requested changes
- Please include the values of the parameters studied in the simulation in the captions of Fig 2-5. This would ease the reading of the text.
- A few words commenting Fig 3& Fig 5 would be welcome in the caption (or in the text): why $|\chi>$ has disappeared for $K=1$ and $K=20$ ? When in the ideal case, the entropy is zero, please write it.