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

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) over bar and an energy omega(sf) below which the system behaves as a Fermi liquid. The ratio of the two determines the dimensionless coupling constant for spin fermion interaction lambda(2) proportional to (g) over bar/omega(sf). We show that lambda 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 lambda, and treat the remaining, O(log lambda) terms in the RG formalism. We apply this technique to study the properties of the spin fermion model in various frequency and temperature regimes. We present the results for the fermionic spectral function, spin susceptibility, optical conductivity and other observables. We compare our results in detail with the normal state data for the cuprates, and argue that the spin fermion model is capable of explaining the anomalous normal state properties of the high T-c materials. We also show that the conventional phi(4) theory of the quantum-critical behaviour is inapplicable in 2D due to the singularity of the phi(4) vertex.