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(omega) similar to omega(alpha) with 1 less than or equal to 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 E-expansion it is seen that there is a range of values alpha(*)(d) less than or equal to alpha less than or equal to 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. (C) 1999 Published by Elsevier Science B.V. All rights reserved.