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:

Phillips, Philip W. ^[1]; Setty, Chandan ^[1]; Zhang, Shuyi ^[1]

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1. Univ. of Illinois at Urbana-Champaign, IL (United States)

Publication Date:

Wed May 02 00:00:00 EDT 2018

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