Quantum-critical theory of the spin-fermion model and its application to cuprates: Normal state analysis

TLDR: In this article, the spin-fermion model near the antiferromagnetic instability in two dimensions was analyzed and it was shown that λ scales with the spin correlation length and diverges at criticality, implying that the conventional perturbative expansion breaks down.

Abstract: We present the full analysis of the normal state properties of the spin-fermion model near the antiferromagnetic instability in two dimensions. The model describes low-energy fermions interacting with their own collective spin fluctuations, which soften at the antiferromagnetic transition. We argue that in 2D, the system has two typical energies—an effective spin-fermion interaction g¯ and an energy ωsf below which the system behaves as a Fermi liquid. The ratio of the two determines the dimensionless coupling constant for spin-fermion interaction λ2 ∝ g¯/ωsf. We show that λ scales with the spin correlation length and diverges at criticality. This divergence implies that the conventional perturbative expansion breaks down. We develop a novel approach to the problem—the expansion in either the inverse number of hot spots in the Brillouin zone, or the inverse number of fermionic flavours—which allows us to explicitly account for all terms which diverge as powers of λ, and treat the remaining, O(log λ) terms...