Eur. Phys. J. D (2016) 70: 35
https://doi.org/10.1140/epjd/e2016-60600-5

Regular Article

Quantum speed limit for a central system in Lipkin-Meshkov-Glick bath

School of Physics, Beijing Institute of Technology, 100081 Beijing, P.R. China

^a e-mail: sbin610@bit.edu.cn

Received: 22 October 2015
Received in final form: 14 December 2015
Published online: 11 February 2016

Abstract

We investigate the physical feature of quantum phase transition (QPT) in a Lipkin-Meshkov-Glick (LMG) model by calculating the quantum speed limit (QSL) time for a central qubit coupled to a LMG bath. We propose that with a suitable choice of the number of spins in bath and the coupling strength between central system and environment, the transition from no speed-up to speed-up of the open system evolution can be achieved at the QPT point, so the QSL is a potential candidate for witnessing QPT of a LMG model. By considering the physical reason for the acceleration, we study the non-Markovianity of the open system and verify that the non-Markovian property can induce the decrease of evolution time, which is also an indication that the phase transition of the system from Markovian to non-Markovian could occur at the QPT point.