We propose that nonequilibrium quantum criticality in open systems under the Born-Markov approximation can be described by a master equation of the Lindblad form. This master equation is derived from a system coupling weakly to a heat bath microscopically and is suggested to provide an approach to study dynamic quantum critical behavior of the system at finite temperatures. We find that the dissipation rate in the equation representing the coupling must be included in the scaling forms as an indispensable additional scaling variable in order to correctly describe the nonequilibrium quantum critical behavior, yet the equilibrium fixed point determines the nonequilibrium critical behavior in the weak coupling limit. Through numerically solving the Lindblad equation for the quantum Ising chain, we affirm these propositions by finite-time scaling forms with the dissipation rate. Nonequilibrium dynamic critical behavior of spontaneous emissions in dissipative open systems at zero temperature near their quantum critical points is discovered and is also described well by the scaling forms.

• Received 19 May 2013
• Revised 11 March 2014

DOI:https://doi.org/10.1103/PhysRevB.89.094108