Absence of a charge diffusion pole at finite energies in an exactly solvable interacting flatband model in $d$ dimensions
Abstract
Motivated by recent bounds for charge diffusion in critical matter, we investigate the following question: What sets the scale for the velocity for diffusing degrees of freedom in a scaleinvariant system? To make our statements precise, here we analyze the diffusion pole in an exactly solvable model for a Mott transition in the presence of a longrange interaction term. To achieve scale invariance, we limit our discussion to the flatband regime. We find in this limit that the diffusion pole, which would normally obtain at finite energy, is pushed to zero energy, resulting in a vanishing of the diffusion constant. This occurs even in the presence of interactions in certain limits, indicating the robustness of this result to the inclusion of a scale in the problem. Consequently, scale invariance precludes any reasonable definition of the diffusion constant. Nonetheless, we do find that a scale can be defined, albeit irrelevant to diffusion, which is the product of the squared band velocity and the density of states.
 Authors:

 Univ. of Illinois at UrbanaChampaign, IL (United States)
 Publication Date:
 Research Org.:
 Energy Frontier Research Centers (EFRC) (United States). Center for Emergent Superconductivity (CES); Brookhaven National Lab. (BNL), Upton, NY (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), Basic Energy Sciences (BES)
 OSTI Identifier:
 1566379
 Alternate Identifier(s):
 OSTI ID: 1435676
 Grant/Contract Number:
 AC0298CH10886; AC0298CH1088
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Physical Review B
 Additional Journal Information:
 Journal Volume: 97; Journal Issue: 19; Journal ID: ISSN 24699950
 Publisher:
 American Physical Society (APS)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; phonons; thermal conductivity; energy storage (including batteries and capacitors); superconductivity; defects; spin dynamics
Citation Formats
Phillips, Philip W., Setty, Chandan, and Zhang, Shuyi. Absence of a charge diffusion pole at finite energies in an exactly solvable interacting flatband model in $d$ dimensions. United States: N. p., 2018.
Web. https://doi.org/10.1103/physrevb.97.195102.
Phillips, Philip W., Setty, Chandan, & Zhang, Shuyi. Absence of a charge diffusion pole at finite energies in an exactly solvable interacting flatband model in $d$ dimensions. United States. https://doi.org/10.1103/physrevb.97.195102
Phillips, Philip W., Setty, Chandan, and Zhang, Shuyi. Wed .
"Absence of a charge diffusion pole at finite energies in an exactly solvable interacting flatband model in $d$ dimensions". United States. https://doi.org/10.1103/physrevb.97.195102. https://www.osti.gov/servlets/purl/1566379.
@article{osti_1566379,
title = {Absence of a charge diffusion pole at finite energies in an exactly solvable interacting flatband model in $d$ dimensions},
author = {Phillips, Philip W. and Setty, Chandan and Zhang, Shuyi},
abstractNote = {Motivated by recent bounds for charge diffusion in critical matter, we investigate the following question: What sets the scale for the velocity for diffusing degrees of freedom in a scaleinvariant system? To make our statements precise, here we analyze the diffusion pole in an exactly solvable model for a Mott transition in the presence of a longrange interaction term. To achieve scale invariance, we limit our discussion to the flatband regime. We find in this limit that the diffusion pole, which would normally obtain at finite energy, is pushed to zero energy, resulting in a vanishing of the diffusion constant. This occurs even in the presence of interactions in certain limits, indicating the robustness of this result to the inclusion of a scale in the problem. Consequently, scale invariance precludes any reasonable definition of the diffusion constant. Nonetheless, we do find that a scale can be defined, albeit irrelevant to diffusion, which is the product of the squared band velocity and the density of states.},
doi = {10.1103/physrevb.97.195102},
journal = {Physical Review B},
number = 19,
volume = 97,
place = {United States},
year = {2018},
month = {5}
}
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