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Resolving the nonequilibrium Kondo singlet in energy- and position-space using quantum measurements
by Andre Erpenbeck, Guy Cohen
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Submission summary
| Authors (as registered SciPost users): | André Erpenbeck |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202102_00003v2 (pdf) |
| Date submitted: | 2021-04-29 14:31 |
| Submitted by: | Erpenbeck, André |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
The Kondo effect, a hallmark of strong correlation physics, is characterized by the formation of an extended cloud of singlet states around magnetic impurities at low temperatures. While many implications of the Kondo cloud's existence have been verified, the existence of the singlet cloud itself has not been directly demonstrated. We suggest a route for such a demonstration by considering an observable that has no classical analog, but is still experimentally measurable: ``singlet weights'', or projections onto particular entangled two-particle states. Using approximate theoretical arguments, we show that it is possible to construct highly specific energy- and position-resolved probes of Kondo correlations. Furthermore, we consider a quantum transport setup that can be driven away from equilibrium by a bias voltage. There, we show that singlet weights are enhanced by voltage even as the Kondo effect is weakened by it. This exposes a patently nonequilibrium mechanism for the generation of Kondo-like entanglement that is inherently different from its equilibrium counterpart.
Author comments upon resubmission
List of changes
A version of the manuscript where all changes are highlighted in color is included in the uploaded document on pages 40-68.
Current status:
Reports on this Submission
Report #2 by Anonymous (Referee 1) on 2021-5-7 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202102_00003v2, delivered 2021-05-07, doi: 10.21468/SciPost.Report.2881
Report
The authors gave a elaborate answer and addressed the questions raised by both referees.
To make the long story below short: Overall it is an very good paper, employing a difficult technique to a tough problem.
The authors did their best to answer all questions to the best of their abilities. I can recommend the paper for publication in the revised version. However, personally I would reconsidering their definition of the Kondo temperature by carefully gauging it against other useful definitions that are developed for various numerical and experimental approaches.
In more detail:
The authors gave a reasonable answer concerning their definition of the Kondo temperature. Apparently, they used the definition from the Bethe-ansatz also requering $U$ to be large! A different estimate is found in chapter 3 in Hewsons book. Here one has to bear in mind that additional corrections to these large $U$ formulas come into play since $U/\pi\Gamma$ is not very large for the parameters in the manuscript. The Kondo temperature is a crossover scale and can always be defined with some arbitrariness.
I am a bit confuse by the statement in the reply: $\Delta=2\Gamma$ as stated in the replay or
$2\times \Gamma/2 =\Gamma$ as written below Eq (58) of the manuscript?
Importantly, all parameters are stated clearly so that the reader can make up her/his own mind.
The spectrum shown in Fig R1 of the reply suggests that indeed the strongly correlated regime is addressed but the AS resonance is still very small (peak hight well below the Hubbard site peaks)
and well below the zero temperature limit predicted by the Friedel sum rule.
This is very encouraging since the NCA is operated in local moment regime in the vicinity or above $T_K$ as I suspected. One can also read off that the NCA underestimates the width of the Kondo resonance as expected for a second order approach in the hybridization strength: higher order processes contribute to the resonance as well.
Just a personal remark: It might be useful for the authors to consult PRL 81, 5226 (1998) for
an operative experimental definition of $T_K$ exploiting the universality of the zero-bias conductance. It was gauged using the results of Costi and Hewson from 1994 and works remarkable well. Employing Goldhaber-Gordon's approach immediately reveals that the choice of $T$ must be above $T_K$.
Why do I emphazise the importance of a proper identification of $T_K$? That becomes clearer when looking into the real-time dynamics which is the main focus of this paper. The other referee asked
"What sets the time scale for the relaxation to the equilibrium? The Kondo temperature is set to 0.8 Gamma, nearly Gamma."
and the authors answer "At equilibrium and in the scaling limit, we typically expect all time and energy scales to be universally determined by $T_K$".
This is only correct when focusing only on the dynamics govern by the low energy excitations of the system which excludes the charge dynamics. Also the spectral function does not only contain a Kondo resonance but also high energy features whose broadening is governed by $\Gamma$. Typically NEQ dynamics of local charges are governed by $\Gamma$, even below for $T\ll T_K$, while the spin dynamics is governed by $T_K$. The reason is obvious: local charge fluctuations are suppressed in the scaling limit. Clearly the charge susceptibility is governed by $1/\Gamma$ while the spin susceptible approaches $1/T_K$ in the scaling limit.
The authors continue in their reply " However, unlike the low-energy features, the transient peak in the energy-resolved singlet weight when starting from an empty dot clearly decays much more slowly (Fig. 3(a))"
I also noticed this slow dynamics when reading the first version of the paper and that was the reason why I instigated a discussion on $T_K$. I suspected that
the spin dynamics reported by the authors indeed governed by $T_K$. However, the authors' estimate for $T_K$ is simply to high such that this point was not recognised by the authors. The authors write in their reply
"one can extract a timescale of ∼ $25\Gamma$", I guess they mean $\tau\approx 25/\Gamma $ which would
be comparable with my estimate of $T_K$ in my first report, suggesting that $\tau\approx 1/T_K$
Question: which other low energy scale should drive the long time dynamics? I suspect that there is non!
Report #1 by Anonymous (Referee 2) on 2021-5-6 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202102_00003v2, delivered 2021-05-06, doi: 10.21468/SciPost.Report.2879
Report
The authors have put much effort into answering the questions of the referees.
I accept the authors' explanation that this manuscript goes beyond existing nonequilibrium studies of the Kondo effect and that the singlet-weights might be a useful tool for future theoretical and experimental studies. Thus, the manuscript fulfills the criteria of SciPost Physics.
I recommend this manuscript for publication in SciPost Physics.