Quantum phase transition in the spin boson model

Quantum phase transitions (QPT) Quantum phase transition have recently become a widespread topic in the realm of modern condensed matter physics. QPT are phase transformations that occur at the absolute zero of temperature and are triggered by varying a temperature-independent control parameter like pressure, doping concentration, or magnetic field. There are various examples of systems showing quantum critical behavior, which include the antiferromagnetic transition in heavy fermion material like , that is brought about by changing the doping [10]. Another prototypical example of a system exhibiting quantum critical behavior is the quantum Hall effect, wherein a two-dimensional electron gas is tuned, via an externally applied magnetic field, through a quantum critical point (QCP) that intervenes between two quantized Hall plateaux. Other examples of QPT include the ferromagnetic transition in metallic magnets as a function of applied pressure and the superconducting transition in thin films. © 2010 Springer-Verlag Berlin Heidelberg.