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Title: Absence of a charge diffusion pole at finite energies in an exactly solvable interacting flat-band 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 scale-invariant 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 long-range interaction term. To achieve scale invariance, we limit our discussion to the flat-band 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:
 [1];  [1];  [1]
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  1. Univ. of Illinois at Urbana-Champaign, 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:  
AC02-98CH10886; AC0298CH1088
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 97; Journal Issue: 19; Journal ID: ISSN 2469-9950
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 flat-band model in $d$ dimensions. United States: N. p., 2018. Web. doi:10.1103/physrevb.97.195102.
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Phillips, Philip W., Setty, Chandan, & Zhang, Shuyi. Absence of a charge diffusion pole at finite energies in an exactly solvable interacting flat-band model in $d$ dimensions. United States. https://doi.org/10.1103/physrevb.97.195102
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Phillips, Philip W., Setty, Chandan, and Zhang, Shuyi. Wed . "Absence of a charge diffusion pole at finite energies in an exactly solvable interacting flat-band model in $d$ dimensions". United States. https://doi.org/10.1103/physrevb.97.195102. https://www.osti.gov/servlets/purl/1566379.
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@article{osti_1566379,
title = {Absence of a charge diffusion pole at finite energies in an exactly solvable interacting flat-band 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 scale-invariant 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 long-range interaction term. To achieve scale invariance, we limit our discussion to the flat-band 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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https://doi.org/10.1103/physrevb.97.195102
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