Decay of Loschmidt Echo at a Critical Point in the Lipkin-Meshkov-Glick model

An analytical expression of the Loschmidt echo in the Lipkin-Meshkov-Glick model is derived in the thermodynamical limit. It is used in the study of the decaying behaviour of the echo at the critical point of a quantum phase transition of the model. It is shown that the echo has a power law decay for relatively long times.