TY - JOUR

T1 - Fermi liquid near Pomeranchuk quantum criticality

AU - Maslov, Dmitrii L.

AU - Chubukov, Andrey V.

PY - 2010/1/11

Y1 - 2010/1/11

N2 - We analyze the behavior of an itinerant two-dimensional Fermi system near a charge nematic (n=2) Pomeranchuk instability in terms of the Landau Fermi-liquid (FL) theory. A key object of our study is the fully renormalized vertex function ΓΩ, related to the Landau interaction function. We derive ΓΩ for a model case of the long-range interaction in the nematic channel. Already within the random-phase approximation (RPA), the vertex is singular near the instability. The full vertex, obtained by resumming the ladder series composed of the RPA vertices, differs from the RPA result by a multiplicative renormalization factor ZΓ, related to the single-particle residue Z and effective-mass renormalization m- /m. We employ the Pitaevski-Landau identities, which express the derivatives of the self-energy in terms of ΓΩ, to obtain and solve a set of coupled nonlinear equations for ZΓ, Z, and m/m. We show that near the transition the system enters a critical FL regime, where ZΓ (1 + gc, 2)1/2 and m /m ≈ 1/Z, where gc,2 is the n=2 charge Landau component which approaches -1 at the instability. We construct the Landau function of the critical FL and show that all but gc,2 Landau components diverge at the critical point. We also show that in the critical regime the one-loop result for the self-energy Σ (K) ∫ dPG (P) D (K-P) is asymptotically exact if one identifies the effective interaction D with the RPA form of ΓΩ.

AB - We analyze the behavior of an itinerant two-dimensional Fermi system near a charge nematic (n=2) Pomeranchuk instability in terms of the Landau Fermi-liquid (FL) theory. A key object of our study is the fully renormalized vertex function ΓΩ, related to the Landau interaction function. We derive ΓΩ for a model case of the long-range interaction in the nematic channel. Already within the random-phase approximation (RPA), the vertex is singular near the instability. The full vertex, obtained by resumming the ladder series composed of the RPA vertices, differs from the RPA result by a multiplicative renormalization factor ZΓ, related to the single-particle residue Z and effective-mass renormalization m- /m. We employ the Pitaevski-Landau identities, which express the derivatives of the self-energy in terms of ΓΩ, to obtain and solve a set of coupled nonlinear equations for ZΓ, Z, and m/m. We show that near the transition the system enters a critical FL regime, where ZΓ (1 + gc, 2)1/2 and m /m ≈ 1/Z, where gc,2 is the n=2 charge Landau component which approaches -1 at the instability. We construct the Landau function of the critical FL and show that all but gc,2 Landau components diverge at the critical point. We also show that in the critical regime the one-loop result for the self-energy Σ (K) ∫ dPG (P) D (K-P) is asymptotically exact if one identifies the effective interaction D with the RPA form of ΓΩ.

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U2 - 10.1103/PhysRevB.81.045110

DO - 10.1103/PhysRevB.81.045110

M3 - Article

AN - SCOPUS:77954831615

SN - 1098-0121

VL - 81

JO - Physical Review B - Condensed Matter and Materials Physics

JF - Physical Review B - Condensed Matter and Materials Physics

IS - 4

M1 - 045110

ER -