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Low-energy excitations and transport functions of the one-dimensional Kondo insulator
by Robert Peters, Roman Rausch
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Submission summary
| Authors (as registered SciPost users): | Robert Peters · Roman Rausch |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2301.08404v1 (pdf) |
| Date submitted: | 2023-01-23 02:34 |
| Submitted by: | Peters, Robert |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
Using variational matrix product states, we analyze the finite temperature behavior of a half-filled periodic Anderson model in one dimension, a prototypical model of a Kondo insulator. We present an extensive analysis of single-particle Green's functions, two-particle Green's functions, and transport functions creating a broad picture of the low-temperature properties. We confirm the existence of energetically low-lying spin excitations in this model and study their energy-momentum dispersion and temperature dependence. We demonstrate that charge-charge correlations at the Fermi energy exhibit a different temperature dependence than spin-spin correlations. While energetically low-lying spin excitations emerge approximately at the Kondo temperature, which exponentially depends on the interaction strength, charge correlations vanish already at high temperatures. Furthermore, we analyze the charge and thermal conductivity at finite temperatures by calculating the time-dependent current-current correlation functions. While both charge and thermal conductivity can be fitted for all interaction strengths by gapped systems with a renormalized band gap, the gap in the system describing the thermal conductivity is generally smaller than the system describing the charge conductivity. Thus, two-particle correlations affect the charge and heat conductivities in a different way resulting in a temperature region where the charge conductivity of this one-dimensional Kondo insulator is already decreasing while the heat conductivity is still increasing.
Current status:
Reports on this Submission
Report #2 by Anonymous (Referee 2) on 2023-3-6 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2301.08404v1, delivered 2023-03-06, doi: 10.21468/SciPost.Report.6855
Strengths
1- Numerically exact variational matrix product states (VMPS) method yields
ground state properties representative of the thermodynamic limit.
2-Excitation spectra/correlation functions are calculated directly on the
real frequency/time axis.
3-Provides evidence for charge-neutral heat carriers in a Kondo insulator and
insight into their physical nature.
Weaknesses
1-The VMPS method is fully controlled only in a limited temperature range above the experimental observations of thermal metallic behavior in charge-insulating Kondo systems.
Report
The manuscript presents a thorough study of the momentum-resolved single-particle spectral function, spin and charge structure factors, and thermodynamic properties (Section 3) supplemented by the analysis of the charge and thermal conductivity (Section 4) of the one-dimensional periodic Anderson model at half filling.
The results of Section 3 nicely illustrate the key physics of the model, i.e., a separation of spin and charge energy scales with increasing Hubbard interaction strength which highlights the difference with respect to a conventional band insulator. However, these results do not contribute anything qualitatively new and can be found in the previous studies using for example a finite-T DMRG method.
What nevertheless argues in favor of publication in SciPost Physics is Section 4
devoted to the analysis of the charge and thermal conductivity at finite temperatures. Specifically, the authors find a temperature region where the charge conductivity of the Kondo insulator is already decreasing while the heat conductivity is still increasing.
This is an important novel result suggesting that experimentally observed thermal metallic behavior in charge-insulating Kondo system can arise solely as a result of strong correlations. Within this scenario, the heat transport is carried by low-energy spin excitations while the charge transport is blocked at temperatures smaller than the charge gap.
These findings provide a simple alternative to theories of charge-neutral fermions invoking topological effects, exotic quasiparticles, or phonons and shall stimulate follow-up work.
Requested changes
1-What is the actual value of the hybridization amplitude V used in the
simulations?
Report #1 by Anonymous (Referee 1) on 2023-3-6 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2301.08404v1, delivered 2023-03-06, doi: 10.21468/SciPost.Report.6852
Strengths
1- Detailed analysis of ground-state and thermodynamics properties of one-dimensional Kondo insulator.
2- Computation of finite-temperature charge and heat transport properties
Weaknesses
1- The finite-temperature parameter range is limited to moderate or high temperatures
Report
The authors investigate the finite-temperature properties of the one-dimensional (1d) Kondo insulator using matrix product states (MPS). First, they are able to reproduce known results at T=0 (spectral functions) as well as thermodynamics at finite T using state-of-the-art numerical techniques. But more interestingly, by computing time-dependent correlation functions, they can obtain the charge and thermal conductivities. It is known for a long-time that in such systems, there are various gaps: charge gap, single-particle gap, spin gap, which can be quite different. As a result, the heat and charge transport behave quite differently too, which could explain recent experiments.
By a careful comparison of exact 2-particle calculations (for charge or spin spectral functions), it is remarkable that qualitative features are found using a simple convolution of the 1-particle Green's function, i.e. without vertex corrections.
I find the paper well written and the results interesting. They are obtained using state-of-the-art numerical techniques. Hence, I recommend it for publication. I do have questions and suggestions though, that could help to improve the presentation:
* Is there any understanding why vertex corrections are negligible for strong coupling ? This could be useful for other techniques which often neglect them.
* In order to perform Fourier transform in time, did you use some trick to avoid artefacts due to the finite tmax ?It would be nice to see (in supplemental) some typical time-dependent correlations at T=0.
* To compute the specific heat, it is written that an MPO form was used for H^2. Is it exact or compressed ? Would it be easier to compute it from the energy e(T) ?
* It is mentioned that different bond dimensions are used for backward/forward evolution, probably due to the local/global nature of the operator. How were the numbers chosen ? In one Appendix, there is a benchmark plot but it would be useful to see how these two parameters are chosen.
* Why are the results not directly comparable to experiments ? Of course materials are 3d, but what about the typical temperature scales ?
Requested changes
1- It would be useful to plot the local density of states N(w) for various T in order to see the appearance of the gap and the emergence of Kondo physics.
2- What is the finite-temperature correlation length for T>0.1 ? Is it the limitation for the numerical technique ?
3- I would not call VMPS as "numerically exact" since usually MPS methods are not guaranteed to converge to the absolute minimum (finding the optimal MPS is NP hard). Of course they do work extremely well for simple models.