Impurity quantum phase transitions

An interesting type of quantum phase transition are boundary transitions where only the degrees of freedom of a subsystem become critical while the bulk remains imcritical. The simplest case is the so-called impurity quantum phase transitions where the free energy contribution of the impurity (or, in general, a zero-dimensional subsystem) becomes singular at the quantum critical point. Such transitions occur in anisotropic Kondo systems, quantum dots, and in spin systems coupled to dissipative baths as examples. Impurity quantum phase transitions require the thermodynamic limit in the bulk (bath) system but are completely independent from possible phase transitions of the bath. A recent review of impurity quantum phase transitions can be found in Ref. 42. 

Let us finally point out that we have focused on bulk quantum phase transitions. Impurity quantum phase transitions" require a separate discussion that is beyond the scope of this chapter (Note, however, that within the DMFT method a bulk quantum many-particle system is mapped onto a self-consistent quantum impurity model.) Some of the methods discussed here such as quantum Monte Carlo can be adapted to impurity problems. Moreover, there are powerful special methods dedicated to impurity problems, most notably Wilson s numerical renormalization group. " " ... 

M. Vojta, Phil. Mag., 86, 1807 (2006). Impurity Quantum Phase Transitions. 

The confinement model is also useful to systematically study effects on an atom or molecule trapped in a microscopic cavity or in fullerenes [72-78]. As mentioned above, some of the system observables undergo changes as a result of spatial confinement. The same situation is found at a nanoscopic scale in artificial systems constructed within semiconductors [79-87,172-188], such as two-dimensional quantum wells, quantum wires and quantum dots. Properties of a hydrogen-like impurity in a 2D quantum well have been investigated by several authors [172,173,185-188], who have concluded that particular features associated with the states, as well as the properties of an impurity, are determined, among other factors, by the size of the confining structure. Other applications of confined systems refer to Metal properties [147,148], astrophysical spectroscopic data [40,146], phase transitions [155], matter embedded in electrical fields [68], nuclear models [164], etc. For a detailed list of references, several review articles [25, 48,54,95,125,127] are available. 

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