k}_1,\omega ),-{\rm Im}\Sigma ({\bf k} _1,\omega ),{\bf 
k}_1=(\pi /2,\pi /2)$ for the value of $J=0.4t$ are represented for the 16$\times $16 site lattice and broadening constant $\eta 
=0.01t$. The comparison of Fig.\[f2\] (b),(c),(d) and the corresponding functions given by Fig.7,8 from Ref.[@horsch] (the same lattice size and $\eta $) demonstrates that the position of peaks of the hole spectral function and their intensities coincide. Some difference is that our $A_h( {\bf 
k}_1,\omega ),$ is more smooth and there are no strong oscillations in our self energy $\Sigma ({\bf k},\omega )$ in the interval $(-2t<\omega <-0.75t).$

The results for the small spin polaron spectral density, real and imaginary parts of the self energy for the characteristic value of energetic parameter $ J=0.7\tau $ are given in Fig. \[f3\] for the symmetrical points ${\bf k} _1=(\pi /2,\pi /2),{\bf 
k}_2=(0,0),{\bf k}_3=(\pi ,\pi )$. The energy broadening parameter is $\eta =0.002$ (we will refer all quantities in units of $\tau $ from now on). We find main common feature in the spectral density for ${\bf k}_1$ and ${\bf k}_2$: a sharp quasiparticle peak exists at the bottom of each spectrum. The position of the QP peak corresponds to the condition ${\rm Re}G^{-1}({\bf k},\omega )=0$ 