Decoherence in a two-level system coupled to a fermion environment with phase transitions

The decoherence process characterized by Loschmidt echo (LE) in a two-level system dephasingly coupled to a fermion environment with phase transitions is studied in this Letter. The results show that the LE of the two-level system may act as a witness of the environment's phase transitions, which is similar to the relation between quantum phase transitions and the LE.