Fermi surface evolution in underdoped cuprates

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Abstract
We consider a two-dimensional Fermi liquid coupled to low-energy commensurate spin fluctuations. At small couplings, the hole Fermi surface is large and centred around (π, π). We show that, as the coupling increases, the shape of the Fermi surface undergoes a substantial evolution and, at strong couplings, the hole Fermi surface consists of small pockets centred at (±π/2, ±π/2). At intermediate couplings, there exist both a large hole Fermi surface centred at (π, π) and four hole pockets, but the quasiparticle residue is small everywhere except for the pieces of the pockets which face the Γ point. The relevance of these results to recent photoemission experiments on YBa2Cu3O7 and Bu2CaCu2O8+x systems, and their relation to the Luttinger theorem are discussed.