Numerical approach to low-doping regime of the t-J model

We develop an efficient numerical method for the description of a single-hole motion in the antiferromagnetic background. The method is free of finite-size effects and allows calculation of physical properties at an arbitrary wavevector. Methodical increase of the functional space leads to results that are valid in the thermodynamic limit. We found good agreement with cumulant expansion, exact- diagonalization approaches on finite lattices as well as self-consistent Born approximations. The method allows a straightforward addition of other inelastic degrees of freedom, such as lattice effects. Our results confirm the existence of a finite quasiparticle weight near the band minimum for a single hole and the existence of string-like peaks in the single-hole spectral function.