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

Abstract

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.

48 pages LaTeX with figures

References in corpus (14)

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Cited by in corpus (5)

• Functional renormalization group approach to correlated fermion systems
• Renormalization in Condensed Matter: Fermionic Systems - from Mathematics to Materials
• Singular Fermi Surfaces II. The Two--Dimensional Case
• Low-Energy Effective Theory at a Quantum Critical Point of the Two-Dimensional Hubbard Model: Mean-Field Analysis
• Honeycomb Hubbard Model at van Hove Filling