Single-hole spectral function and spin-charge separation in the $t-J$ model

Worm algorithm Monte Carlo simulations of the hole Green function with subsequent spectral analysis were performed for $0.1<~J/t<~0.4$ on lattices with up to $L\times L=32\mathrm{}\times 32$ sites at a temperature as low as $T=J/40,$ and present, apparently, the hole spectral function in the thermodynamic limit. Spectral analysis reveals a δ-function-sharp quasiparticle peak at the lower edge of the spectrum that is incompatible with the power-law singularity and thus rules out the possibility of spin-charge separation in this parameter range. Spectral continuum features two peaks separated by a gap $\sim 4÷5\hspace{0.5em}t.\mathrm{}$