### 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, 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.

Original language | English (US) |
---|---|

Article number | 195102 |

Journal | Physical Review B |

Volume | 97 |

Issue number | 19 |

DOIs | |

State | Published - May 2 2018 |

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### ASJC Scopus subject areas

- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics

### Cite this

*Physical Review B*,

*97*(19), [195102]. https://doi.org/10.1103/PhysRevB.97.195102

**Absence of a charge diffusion pole at finite energies in an exactly solvable interacting flat-band model in d dimensions.** / Phillips, Philip W.; Setty, Chandan; Zhang, Shuyi.

Research output: Contribution to journal › Article

*Physical Review B*, vol. 97, no. 19, 195102. https://doi.org/10.1103/PhysRevB.97.195102

}

TY - JOUR

T1 - Absence of a charge diffusion pole at finite energies in an exactly solvable interacting flat-band model in d dimensions

AU - Phillips, Philip W.

AU - Setty, Chandan

AU - Zhang, Shuyi

PY - 2018/5/2

Y1 - 2018/5/2

N2 - 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, 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.

AB - 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, 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.

UR - http://www.scopus.com/inward/record.url?scp=85047013828&partnerID=8YFLogxK

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U2 - 10.1103/PhysRevB.97.195102

DO - 10.1103/PhysRevB.97.195102

M3 - Article

AN - SCOPUS:85047013828

VL - 97

JO - Physical Review B

JF - Physical Review B

SN - 2469-9950

IS - 19

M1 - 195102

ER -