Reentrant enhancement of quantum fluctuations for symmetric environmental coupling

The system-plus-reservoir (SPR) model is the most common and effective approach to study quantum dissipative effects. Indeed, it makes quantization possible by considering the whole energy-conserving system, while the reservoir's degrees of freedom, assumed to be harmonic, can be traced out by the path-integral technique, leading to a formulation that only includes the system of interest. In the standard SPR model the environment is only coupled with the system's coordinate and turns out to quench its quantum fluctuations. However, there are physical systems coupled with an environment whose "coordinates" and "momenta" can be completely interchangeable (e.g., magnets), so an SPR coupling must symmetrically affect both canonical variables. In this paper such a general environmental coupling is studied in the case of a harmonic oscillator. It is found that quantum fluctuations are generally enhanced by environmental coupling with an unexpected nonmonotonic behavior. This leads one to speculate about the possibility that spin-lattice coupling could drive the two-dimensional Heisenberg antiferromagnet to reach its quantum-critical point.