Spin-wave condensation and quantum melting of long-range antiferromagnetic order in the t-J model

Ground-state wave function of the two-dimensional t-J model is found at doping close to half filling. It is shown that the condensation of Cooper pairs (superconducting pairing of mobile holes) and the condensation of spin waves into the spin-liquid state are closely connected. The effective spectrum of S = 1 excitations, spin-wave pseudogap Delta(M) magnetic correlation length xi(M), and static magnetic formfactor S-M(q) are calculated.