Abstract
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, χ(q,ω), and to the quasiparticle spectral function,
A(k,ω), are divergent near the transition. We identify and sum the
series of most singular diagrams, and obtain a solution for χ(q,ω)
and an approximate solution for A(k,ω). We show that (i) A(k) at
a given, small ω has an extra peak at k=kF+π (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-δ and Bi2Sr2CaCu2O8 systems is discussed.
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