A Renormalization-Group approach to the Coulomb Gap

Physics – Condensed Matter

Scientific paper

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16 pages, LaTeX. Diagrams available on request from srj1001@phy.cam.ac.uk. Changes to figure 4 and second half of section 6

Scientific paper

10.1088/0953-8984/8/19/011

The free energy of the Coulomb Gap problem is expanded as a set of Feynman diagrams, using the standard diagrammatic methods of perturbation theory. The gap in the one-particle density of states due to long-ranged interactions corresponds to a renormalization of the two-point vertex function. By collecting the leading order logarithmic corrections we have derived the standard result for the density of states in the critical dimension, d=1. This method, which is shown to be identical to the approach of Thouless, Anderson and Palmer to spin glasses, allows us to derive the strong-disorder behaviour of the density of states. The use of the renormalization group allows this derivation to be extended to all disorders, and the use of an epsilon-expansion allows the method to be extended to d=2 and d=3. We speculate that the renormalization group equations can also be derived diagrammatically, allowing a simple derivation of the crossover behaviour observed in the case of weak disorder.

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