Chemistry Reference
In-Depth Information
modes at the same footing. This mechanism is discussed in detail in Ref. 9, and
it is important for metallic quantum ferromagnets as an example.
Deconfined Quantum Criticality
Certain two-dimensional
S
2
quantum antiferromagnets can undergo a
direct continuous quantum phase transition between two ordered phases, an
antiferromagnetic N´el phase and the so-called valence-bond ordered phase
(where translational invariance is broken). This is in contradiction to Landau
theory, which predicts phase coexistence, an intermediate phase, or a first-
order transition, if any. The continuous transition is the result of topological
defects that become spatially deconfined at the critical point and are not con-
tained in an LGW description. Recently, there has been a great interest in the
resulting deconfined quantum critical points.
35
¼
Heavy-Fermion Quantum Criticality
Nonconventional quantum critical point scenarios may also be impor-
tant for understanding the magnetic transitions in heavy-fermion systems. In
experiments,
36
many of these materials show pronounced deviations from the
predictions of the standard LGW theory of metallic quantum phase transi-
tions.
37,38
The breakdown of the conventional approach in these systems
may be due to Kondo fluctuations. The standard theory
37,38
assumes that
the heavy quasi-particles (which arise from Kondo hybridization between f
electrons and conduction electrons) remain intact across the transition. How-
ever, there is now some fairly direct experimental evidence (from de-Haas-
van-Alphen and Hall measurements) for the Kondo effect breaking down right
at the magnetic transition in some materials. This phenomenon cannot be
described in terms of the magnetic order parameter fluctuations contained in
the LGW theory. Several alternative scenarios are being developed, including
the so-called local critical point,
39
and the fractionalized Fermi liquid leading
to one of the above-mentioned deconfined quantum critical points.
40,41
A
complete field theory for these transitions has not yet been worked out.
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 uncritical. 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 cri-
tical 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.
