Renormalization group analysis of the quantum non-linear sigma model with a damping term

We investigate the behavior of the zero-temperature quantum non-linear sigma model in d dimensions in the presence of a damping term of the form f(w)~ |w|^alpha, with 1 \le alpha <2. We find two fixed points: a spin-wave fixed point FP1 showing a dynamic scaling exponent z=1 and a dissipative fixed point FP2 with z>1. In the framework of the \epsilon-expansion it is seen that there is a range of values alpha_*(d) \le alpha \le 2 where the point FP1 is stable with respect to FP2, so that the system realizes a z=1 quantum critical behavior even in the presence of a dissipative term. However, reasonable arguments suggest that in d=2 this range is very narrow. In the broken symmetry phase we discuss a phenomenological scaling approach, treating damping as a perturbation of the ordered ground state. The relation of these results with the pseudogap effect observed in underdoped layered cuprates is discussed.