TY - JOUR

T1 - Fermion loops and improved power-counting in two-dimensional critical metals with singular forward scattering

AU - Holder, Tobias

AU - Metzner, Walter

N1 - Publisher Copyright:
©2015 American Physical Society.

PY - 2015/12/22

Y1 - 2015/12/22

N2 - We analyze general properties of the perturbation expansion for two-dimensional quantum critical metals with singular forward scattering, such as metals at an Ising nematic quantum critical point and metals coupled to a U(1) gauge field. We derive asymptotic properties of fermion loops appearing as subdiagrams of the contributing Feynman diagrams - for large and small momenta. Substantial cancellations are found in important scaling limits, which reduce the degree of divergence of Feynman diagrams with boson legs. Implementing these cancellations, we obtain improved power-counting estimates that yield the true degree of divergence. In particular, we find that perturbative contributions to the boson self-energy are generally ultraviolet convergent for a dynamical critical exponent z<3, and divergent beyond three-loop order for z≥3.

AB - We analyze general properties of the perturbation expansion for two-dimensional quantum critical metals with singular forward scattering, such as metals at an Ising nematic quantum critical point and metals coupled to a U(1) gauge field. We derive asymptotic properties of fermion loops appearing as subdiagrams of the contributing Feynman diagrams - for large and small momenta. Substantial cancellations are found in important scaling limits, which reduce the degree of divergence of Feynman diagrams with boson legs. Implementing these cancellations, we obtain improved power-counting estimates that yield the true degree of divergence. In particular, we find that perturbative contributions to the boson self-energy are generally ultraviolet convergent for a dynamical critical exponent z<3, and divergent beyond three-loop order for z≥3.

UR - http://www.scopus.com/inward/record.url?scp=84954125144&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.92.245128

DO - 10.1103/PhysRevB.92.245128

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AN - SCOPUS:84954125144

SN - 1098-0121

VL - 92

JO - Physical Review B - Condensed Matter and Materials Physics

JF - Physical Review B - Condensed Matter and Materials Physics

IS - 24

M1 - 245128

ER -