paper

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

arXiv:cond-mat/9811392 · doi:10.1016/S0550-3213(99)00340-5

Abstract

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 ε-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.

Final version, to be published in Nucl. Phys. B [FS] (26 pages, 5 figures). Analysis extended to an arbitrary number N of field components, added Comments on the d=0, N=2 case to make contact with the physics of dissipative macroscopic quantum tunnelling and of spin chains

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