Quantum critical behavior in itinerant electron systems: Eliashberg theory and instability of a ferromagnetic quantum critical point
By J. Rech, C. Pépin, A. Chubukov. 2006
133 citations recorded by the source corpus.
We consider the problem of fermions interacting with gapless long-wavelength collective bosonic modes. The theory describes, among other cases, a ferromagnetic quantum-critical point (QCP) and a QCP towards nematic ordering. We construct a controllable expansion at the QCP in two steps: we first create a non-Fermi-liquid ``zero-order'' Eliashberg-type theory, and then demonstrate that the residual interaction effects are small. We prove that this approach is justified under two conditions: the interaction should be smaller than the fermionic bandwidth, and either the band mass ${m}_{B}$ should be much smaller than $m={k}_{F}∕{v}_{F}$, or the number of fermionic flavors $N$ should be large. For an SU(2) symmetric ferromagnetic QCP, we find that the Eliashberg theory itself includes a set of singular renormalizations which can be understood as a consequence of an effective long-range dynamic interaction between quasiparticles, generated by the Landau damping term. These singular renormalizations give rise to a negative nonanalytic ${q}^{3∕2}$ correction to the static spin susceptibility, and destroy a ferromagnetic QCP. We demonstrate that this effect can be understood in the framework of the ${\ensuremath{\phi}}^{4}$ theory of quantum criticality. We also show that the nonanalytic ${q}^{3∕2}$ correction to the bosonic propagator is specific to the SU(2) symmetric case. For systems with a scalar order parameter, the ${q}^{3∕2}$ contributions from individual diagrams cancel out in the full expression of the susceptibility, and the QCP remains stable.
Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics
View Paper: https://www.semanticscholar.org/paper/39505e4c2d3c676d459ba99580d7096ca3a46426
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In Atomic and Molecular Physics, and Optics
In Condensed Matter Physics
Citations in the corpus
- Functional renormalization group approach to correlated fermion systems (2011, methodology): “…coupled boson-fermion systems exhibiting quantum criticality have already been analyzed by various methods; see, for example, Abanov et al. (2003); Belitz et al. (2001a,b); Huh and Sachdev (2008); Kaul and Sachdev (2008); Metlitski and Sachdev (2010a,b); Rech et al. (2006); Vojta et al. (2000).”