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arXiv · 1706.00015

Absence of a Charge Diffusion Pole at Finite Energies in an Exactly Solvable Interacting Flat Band Model in d-dimensions

Philip Phillips·Chandan Setty·Shuyi Zhang
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Abstract

Motivated by recent bounds for charge diffusion in critical matter, we investigate the question: What sets the scale for charge diffusion 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, all be it, irrelevant to diffusion, which is the product of the squared band velocity and the density of states.

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Philip Phillips, Chandan Setty, Shuyi Zhang. 2017-06-26. Absence of a Charge Diffusion Pole at Finite Energies in an Exactly Solvable Interacting Flat Band Model in d-dimensions. https://doi.org/10.1103/physrevb.97.195102

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