Singular Fermi Surfaces I. General Power Counting and Higher Dimensional Cases

Details Singular Fermi Surfaces I. General Power Counting and Higher Dimensional Cases Singular Fermi Surfaces I. General Power Counting and Higher Dimensional Cases

2007-06-12

arxiv.org/abs/0706.1786v1

Physics

Mathematical Physics

48 pages LaTeX with figures

Scientific paper

10.1142/S0129055X08003274

We prove regularity properties of the self-energy, to all orders in perturbation theory, for systems with singular Fermi surfaces which contain Van Hove points where the gradient of the dispersion relation vanishes. In this paper, we show for spatial dimensions $d \ge 3$ that despite the Van Hove singularity, the overlapping loop bounds we proved together with E. Trubowitz for regular non--nested Fermi surfaces [J. Stat. Phys. 84 (1996) 1209] still hold, provided that the Fermi surface satisfies a no-nesting condition. This implies that for a fixed interacting Fermi surface, the self-energy is a continuously differentiable function of frequency and momentum, so that the quasiparticle weight and the Fermi velocity remain close to their values in the noninteracting system to all orders in perturbation theory. In a companion paper, we treat the more singular two-dimensional case.

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