Effect of a nonzero temperature on quantum critical points in itinerant fermion systems

TLDR

I reexamine Hertz’s theory of quantum phase transitions in itinerant fermion systems. I determine when it is permissible to integrate out the fermions and analyze the critical phenomena via an effective bosonic theory that retains only ordering‑field fluctuations. By solving appropriate scaling equations I obtain the distinct regimes of correlation‑length and free‑energy behavior in the disordered phase of the effective bosonic theory. The results differ from Hertz’s predictions, align with recent dilute Bose‑gas studies, and suggest relevance to heavy‑fermion materials.

Abstract

I reexamine the work of Hertz on quantum phase transitions in itinerant fermion systems. I determine when it is permissible to integrate out the fermions and analyze the critical phenomena via an effective bosonic theory in which only fluctuations of the ordering field are explicitly retained. By solving appropriate scaling equations I obtain the different regimes of behavior of the correlation length and free energy in the disordered phase of the effective bosonic theory. The results in many cases differ from those of Hertz, but make contact with more recent work on the dilute Bose gas. I briefly discuss the relevance of the results to heavy-fermion materials.