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Lowenergy excitations and transport functions of the onedimensional 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:  20230123 02:34 
Submitted by:  Peters, Robert 
Submitted to:  SciPost Physics 
Ontological classification  

Academic field:  Physics 
Specialties: 

Approaches:  Theoretical, Computational 
Abstract
Using variational matrix product states, we analyze the finite temperature behavior of a halffilled periodic Anderson model in one dimension, a prototypical model of a Kondo insulator. We present an extensive analysis of singleparticle Green's functions, twoparticle Green's functions, and transport functions creating a broad picture of the lowtemperature properties. We confirm the existence of energetically lowlying spin excitations in this model and study their energymomentum dispersion and temperature dependence. We demonstrate that chargecharge correlations at the Fermi energy exhibit a different temperature dependence than spinspin correlations. While energetically lowlying 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 timedependent currentcurrent 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, twoparticle correlations affect the charge and heat conductivities in a different way resulting in a temperature region where the charge conductivity of this onedimensional Kondo insulator is already decreasing while the heat conductivity is still increasing.
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Reports on this Submission
Anonymous Report 2 on 202336 (Invited Report)
 Cite as: Anonymous, Report on arXiv:2301.08404v1, delivered 20230306, 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.
2Excitation spectra/correlation functions are calculated directly on the
real frequency/time axis.
3Provides evidence for chargeneutral heat carriers in a Kondo insulator and
insight into their physical nature.
Weaknesses
1The VMPS method is fully controlled only in a limited temperature range above the experimental observations of thermal metallic behavior in chargeinsulating Kondo systems.
Report
The manuscript presents a thorough study of the momentumresolved singleparticle 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 onedimensional 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 finiteT 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 chargeinsulating Kondo system can arise solely as a result of strong correlations. Within this scenario, the heat transport is carried by lowenergy spin excitations while the charge transport is blocked at temperatures smaller than the charge gap.
These findings provide a simple alternative to theories of chargeneutral fermions invoking topological effects, exotic quasiparticles, or phonons and shall stimulate followup work.
Requested changes
1What is the actual value of the hybridization amplitude V used in the
simulations?
Anonymous Report 1 on 202336 (Invited Report)
 Cite as: Anonymous, Report on arXiv:2301.08404v1, delivered 20230306, doi: 10.21468/SciPost.Report.6852
Strengths
1 Detailed analysis of groundstate and thermodynamics properties of onedimensional Kondo insulator.
2 Computation of finitetemperature charge and heat transport properties
Weaknesses
1 The finitetemperature parameter range is limited to moderate or high temperatures
Report
The authors investigate the finitetemperature properties of the onedimensional (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 stateoftheart numerical techniques. But more interestingly, by computing timedependent correlation functions, they can obtain the charge and thermal conductivities. It is known for a longtime that in such systems, there are various gaps: charge gap, singleparticle 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 2particle calculations (for charge or spin spectral functions), it is remarkable that qualitative features are found using a simple convolution of the 1particle Green's function, i.e. without vertex corrections.
I find the paper well written and the results interesting. They are obtained using stateoftheart 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 timedependent 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 finitetemperature 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.