QUASI-PARTICLE SPECTRUM IN A NEARLY ANTIFERROMAGNETIC FERMI-LIQUID - SHADOW AND FLAT BANDS

We consider a two-dimensional Fermi liquid in the vicinity of a spin-density-wave transition to a phase with commensurate antiferromagnetic long-range order. We assume that near the transition, the Fermi surface is large and crosses the magnetic Brillouin zone boundary. We show that under these conditions, the self-energy corrections to the dynamical spin susceptibility, chi(q, omega), and to the quasiparticle spectral function, A (k, omega), are divergent near the transition. We identify and sum the series of most singular diagrams, and obtain a solution for chi(q, omega) and an approximate solution for A (k, omega). We show that (i) A(k) at a given, small omega has an extra peak at k=k(F)+pi (shadow band), and (ii) the dispersion near the crossing points is much flatter than for free electrons. The relevance of these results to recent photoemission experiments in YBa2Cu3O7-delta and Bi2Sr2 CaCu2O8 systems is discussed.