Condensation energy in the spin-fermion model for cuprates

Abstract

We use the Scalapino-White relation between the condensation energy and the difference between the dynamical structure factor in the normal and the superconducting states to compute the condensation energy in the spin-fermion model. We show that at strong coupling, the extra low-frequency spectral weight associated with the resonance peak in the dynamical structure factor in a superconductor is compensated only at energies $\sim J$ which are much larger than the superconducting gap $\Delta$. We argue that in this situation, the condensation energy is large and well accounts for the data for cuprates.