The Open-System Dicke-Model Quantum Phase Transition with a Sub-Ohmic Bath

We show that the critical exponent of a quantum phase transition in a damped-driven open system is determined by the spectral density function of the reservoir. We consider the open-system variant of the Dicke model, where the driven boson mode and also the large N-spin couple to independent reservoirs at zero temperature. The critical exponent, which is $1$ if there is no spin-bath coupling, decreases below 1 when the spin couples to a sub-Ohmic reservoir.