  Semiflexible polymer models are widely used as a paradigm to understand
structural phases in biomolecules including folding of proteins. Since stable
knots are not so common in real proteins, the existence of stable knots in
semiflexible polymers has not been explored much. Here, via extensive replica
exchange Monte Carlo simulation we investigate the same for a bead-stick and a
bead-spring homopolymer model that covers the whole range from flexible to
stiff. We establish the fact that the presence of stable knotted phases in the
phase diagram is dependent on the ratio $r_b/r_{\rm{min}}$ where $r_b$ is the
equilibrium bond length and $r_{\rm{min}}$ is the distance for the strongest
nonbonded contacts. Our results provide evidence for both models that if the
ratio $r_b/r_{\rm{min}}$ is outside a small window around unity then depending
on the bending stiffness one always encounters stable knotted phases along with
the usual frozen and bent-like structures at low temperatures. These findings
prompt us to conclude that knots are generic stable phases in semiflexible
polymers.

Soft Condensed Matter;Statistical Mechanics;Computational Physics