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
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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.
In: Physical Review B, Vol. 97, No. 19, 195102, 02.05.2018.Research output: Contribution to journal › Article
}
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.
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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 -