Numerical approach to the 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 the calculation of physical properties at an arbitrary wave vector. A 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 stringlike peaks in the single-hole spectral function.