  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.

Strongly Correlated Electrons;Superconductivity