# 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:

- 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) (SC-22)

- 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.
```

```
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. doi: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 flat-band model in $d$ dimensions". United States. doi: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 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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