Pseudogaps and magnetic properties of the two-dimensional t-J model
  We apply the modified spin-wave theory with the constraint of zero staggered magnetization to investigate normal-state spectral and magnetic properties of the 2D t-J model in the paramagnetic state. A set of self-energy equations for hole and magnon Green's functions is solved numerically in the self-consistent Born approximation. The constraint can be fulfilled in the ranges of hole concentrations 0.02 < x < 0.17 and temperatures T < 150 K. In this region the hole spectrum differs from a conventional metallic spectrum which is manifested in the variation with x of the quasiparticle weights of states and in the violation of Luttinger's theorem. With decreasing x from x = 0.17 hidden parts appear in the hole Fermi surface which can be interpreted as the opening of a pseudogap near (pi,0). Obtained size, symmetry and concentration dependence of the pseudogap are in agreement with photoemission data in Bi2212. Calculated temperature dependencies of the spin correlation length, spin-lattice relaxation times at the Cu and O sites, and static susceptibility are typical for the quantum disordered regime with a pseudogap in the spectrum of magnetic excitations. These quantities are in qualitative and in some cases in quantitative agreement with experiment in underdoped YBa2Cu3O(6+y). At x > 0.12 the considered phase borders the phase of conventional metal. 
A. Sherman and M. Schreiber