The structures of a single polyethylene chain were investigated using all-atom molecular dynamics simulations with a series of cutoff distances. We found that a long single chain with a short cutoff distance undergoes coil, globule, and crystal states during a continuous cooling process. The globule state vanishes for short chains less than a certain length where there is large conformational fluctuation. A tight-folding model was applied to analyze the folded structures, and the re-entry modes show that a shorter chain prefers the nearest folding while a longer one prefers the second or third nearest folding. Our results show that a single polyethylene chain can exhibit condensed phenomena of state transitions, which could be heuristic for single-chain physics and polymer crystallization.