Dynamic equilibrium of collective degrees of freedom in strongly correlated quantum matter

Strongly correlated quantum systems may assume states stabilized by dynamic equilibrium of competing collective degrees of freedom. As a first example we consider the Kondo effect, which may be viewed as governed by a subtle balance of an infinite growth of the exchange coupling constant controled by an increasing local spin relaxation rate, leading to a Fermi liquid stable fixed point at low temperatures. As a second example the quantum critical behavior in antiferromagnetic metals will be considered. It is often found experimentally that the quasiparticle effective mass appears to diverge at the quantum critical point in spite of the fact that the critical spin fluctuations seem to be in the weak coupling domain – a contradiction. It will be shown that the feedback of the diverging mass into the spin fluctuation spectrum allows to establish a balance of the fermionic and bosonic singular degrees of freedom, leading to strong-coupling type quantum critical behavior. The resulting self-consistent theory obeys hyper-scaling of the dominant fermionic degrees of freedom, while the bosonic interaction is still in the weak coupling domain. Excellent agreement is found with experiment for the two candidate cases CeCu_6-xAu_x and YbRh₂Si₂.