The rotationally invariant approximation for the two-dimensional t-J model

Using the description in terms of the Hubbard operators hole and spin Green's functions of the two-dimensional t-J model are calculated in an approximation which retains the rotation symmetry of the spin susceptibility in the paramagnetic state and has no predefined magnetic ordering. In this approximation, Green's functions are represented by continued fractions which are interrupted with the help of the decoupling corrected by the constraint of zero site magnetization in the paramagnetic state. Results obtained in this approach for an undoped 32x32 lattice (the Heisenberg model) and for one hole in a 4x4 lattice are in good agreement with Monte Carlo and exact diagonalization data, respectively. In the limit of heavy doping the hole spectrum described by the obtained formulas acquires features of the spectrum of weakly correlated excitations.