TY - JOUR

T1 - Quantum critical behavior in itinerant electron systems

T2 - Eliashberg theory and instability of a ferromagnetic quantum critical point

AU - Rech, Jérôme

AU - Pépin, Catherine

AU - Chubukov, Andrey V.

PY - 2006

Y1 - 2006

N2 - 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 mB should be much smaller than m= kF vF, 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 q3 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 4 theory of quantum criticality. We also show that the nonanalytic q3 2 correction to the bosonic propagator is specific to the SU(2) symmetric case. For systems with a scalar order parameter, the q3 2 contributions from individual diagrams cancel out in the full expression of the susceptibility, and the QCP remains stable.

AB - 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 mB should be much smaller than m= kF vF, 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 q3 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 4 theory of quantum criticality. We also show that the nonanalytic q3 2 correction to the bosonic propagator is specific to the SU(2) symmetric case. For systems with a scalar order parameter, the q3 2 contributions from individual diagrams cancel out in the full expression of the susceptibility, and the QCP remains stable.

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U2 - 10.1103/PhysRevB.74.195126

DO - 10.1103/PhysRevB.74.195126

M3 - Article

AN - SCOPUS:33751540165

SN - 2469-9950

VL - 74

JO - Physical Review B

JF - Physical Review B

IS - 19

M1 - 195126

ER -