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Kondo spectral functions at low-temperatures: A dynamical-exchange-correlation-field perspective.
by Zhen Zhao
Submission summary
| Authors (as registered SciPost users): | Zhen Zhao |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202407_00039v2 (pdf) |
| Date submitted: | 2024-10-25 20:45 |
| Submitted by: | Zhao, Zhen |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We calculate the low-temperature spectral function of the symmetric single impurity Anderson model using a recently proposed dynamical exchange-correlation (xc) field formalism. The xc field, coupled to the one-particle Green's function, is obtained through analytic analysis and numerical extrapolation based on finite clusters. In the Kondo regime, the xc field is modeled by an ansatz that takes into account the different asymptotic behaviors in the small- and large-time regimes. The small-time xc field contributes to the Hubbard side-band, whereas the large-time to the Kondo resonance. We illustrate these features in terms of analytical and numerical calculations for small- and medium-size finite clusters, and in the thermodynamic limit. The results indicate that the xc field formalism provides a good trade-off between accuracy and complexity in solving impurity problems. Consequently, it can significantly reduce the complexity of the many-body problem faced by first-principles approaches to strongly correlated materials.
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- Provide a novel and synergetic link between different research areas.
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Author comments upon resubmission
I herewith resubmit the manuscript "Kondo spectral functions at low-temperatures: A dynamical-exchange-correlation-field perspective" for publication in SciPost Physics.
I would like to thank the referees for their insightful reports. The referees provided general observations as well as detailed questions, some of which helped us improve our original approach and inspired us to deepen our understanding of the results. In accordance with our replies sent to the referee reports, text changes have been made in the revised manuscript, addressing the referees' observations and suggestions to make the manuscript more suitable for publication in SciPost Physics.
Finally, I would like to thank you for your consideration and handling of this manuscript.
With best regards,
Z. Zhao
List of changes
1. Changes in Sec. 2
A relation between the dynamical xc field and the self-energy in frequency domain has been added.
An explanation of the exact constraint of the dynamical xc hole has been included.
2. Changes in Sec. 2.1
The use of the Lehmann representation of the Green's function is now explicitly pointed out.
Notations related to spin indices have been revised for consistency through the manuscript.
3. Changes in Sec. 2.2
It is now explicitly stated that the xc field (Eq. 27 in the revised manuscript) is derived by applying the Lehmann representation of the Green's function to its equation of motion and solving for the xc field.
4. Changes in Sec. 3.1
For the dimer, the term "Kondo regime" has been replaced with "large interaction regime" for precision.
The statement in the end of this subsection regarding the temperature-induced broadening of the spectral peaks has been revised.
5. Changes in Sec. 3.2
In the end of this subsection, additional discussions have been added regarding the fact that finite cluster results provide insights about the xc field in the small-time regime. For the SIAM, the Kondo resonance is related to the large-time behavior of the xc field.
6. Changes in Sec. 3.3
An ansatz capturing both small- and large-time behavior of the xc field has been proposed. The Green's function can now be calculated by directly integrating the ansatz over time, which improves the treatment in the original manuscript, where a low-order expansion was applied.
The way of calculating the xc field with negative time using the particle-hole symmetry is now explicitly described.
Interpretations of the ansatz parameters (Eqs. 43-45 in the revised manuscript) are explained in more details.
Additional comments on the hyperbolic-tangent functional fitting are provided.
The treatment of the ansatz parameters at low-temperatures (Eqs. 47-51 in the revised manuscript) is now improved. A Fermi-liquid-theory-based expression for the Kondo peak half-width in the literature is now used as reference.
NRG results adapted from some literature have been added in Fig. 4 and Fig.5 for better comparison. With the improved treatment at low-temperatures, we now plot the spectral functions in Fig. 5 for additional temperature values. We also expand discussions about the detailed difference between our results and those from NRG.
7. Changes in Sec. 4
Discussions on the asymptotic behaviors of the xc field in the small- and large-time regimes have been added.
8. Changes in Appendix C
A detailed explanation of how the Green's function on a finite cluster at zero-temperature can be calculated using the TDVP method is provided.
9. Changes in Appendix D
We derive the Green's function using the improved ansatz of the xc field, showing that no low-order expansion is involved.
10. Changes in References
Additional citations have been added regarding the reference expression for the Kondo peak half-width in Sec. 3.3.