Quantum critical behavior in itinerant electron systems -- Eliashberg theory and instability of a ferromagnetic quantum-critical point

Abstract

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 new, 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 $m=p_F/v_F$, 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 quasi-particles, generated by the Landau damping term. These singular renormalizations give rise to a negative non-analytic $q^{3/2}$ correction to the static spin susceptibility, and destroy a ferromagnetic QCP. We demonstrate that this effect can be understood in the framework of the ${\varphi }^4$ theory of quantum criticality. We also show that the non-analytic $q^{3/2}$ 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.

37 pages, 10 figs

Cited by in corpus (17)

• Theory of the nodal nematic quantum phase transition in superconductors
• Electrical resistivity near Pomeranchuk instability in two dimensions
• Nonanalytic paramagnetic response of itinerant fermions away and near a ferromagnetic quantum phase transition
• Selective Mott transition and heavy fermions
• Spin-triplet pairing instability of the spinon Fermi surface in a U(1) spin liquid
• Renormalization group for phases with broken discrete symmetry near quantum critical points
• Non-analytic behavior of 2D itinerant ferromagnets
• Fermionic propagators for 2D systems with singular interactions
• Universal non-linear conductivity near to an itinerant-electron ferromagnetic quantum critical point
• Cooper channel and the singularities in the thermodynamics of a Fermi liquid
• Model of Quantum Criticality in He3 bilayers Adsorbed on graphite
• Interaction Correction of Conductivity Near a Ferromagnetic Quantum Critical Point
• Interaction effects in 2D electron gas in a random magnetic field: Implications for composite fermions and quantum critical point
• Spin-gapped incoherent metal with preformed pairing in the doped antiferromagnetic Mott insulator
• He3 bi-layers as a simple example of de-confinement
• Fermionization for charge degrees of freedom and bosonization of spin degrees of freedom in the SU(2) slave-boson theory
• Effect of Spin Fluctuations on Phonon-Mediated Superconductivity in the Vicinity of a Quantum Critical Point