We propose a new parametrization of the four-point vertex function in the one-loop one-particle irreducible renormalization group (RG) scheme for fermions. It is based on a decomposition of the effective two-fermion interaction into fermion bilinears that interact via exchange bosons. The numerical computation of the RG flow of the boson propagators reproduces the leading weak coupling instabilities of the two-dimensional Hubbard model at Van Hove filling, as they were obtained by a temperature RG flow in [12]. Instead of regularizing with temperature, we here use a soft frequency Ω-regularization that likewise does not artificially suppress ferromagnetism. Besides being more efficient than previous N -patch schemes, this parametrization also reduces the ambiguities in introducing boson fields.
We present a functional renormalization group calculation for the two-dimensional (t,t )-Hubbard model at Van Hove filling. Using a channel decomposition we describe the momentum and frequency dependence of the vertex function in the normal phase. Compared to previous studies that neglect frequency dependencies we find higher pseudocritical scales and a smaller region of d-wave superconductivity. A large contribution to the effective interaction is given by a forward-scattering process with finite frequency exchange. We test different frequency parametrizations and in a second calculation include the frequency dependence of the imaginary self-energy. We also generalize the channel decomposition to frequency-dependent fermion-boson vertex functions.
We analyze effective d-wave interactions in the two-dimensional extended
Hubbard model at weak coupling and small to moderate doping. The interactions
are computed from a renormalization group flow. Attractive d-wave interactions
are generated via antiferromagnetic spin fluctuations in the pairing and charge
channels. Above Van Hove filling, the d-wave charge interaction is maximal at
incommensurate diagonal wave vectors, corresponding to nematic fluctuations
with a diagonal modulation. Below Van Hove filling a modulation along the
crystal axes can be favored. The nematic fluctuations are enhanced by the
nearest-neighbor interaction in the extended Hubbard model, but they always
remain smaller than the dominant antiferromagnetic, pairing, or charge density
wave fluctuations.Comment: 8 pages, 4 figures; figures improve
For disordered elastic manifolds in the ground state (equilibrium) we obtain the critical exponents for the roughness and the correction-to-scaling up to 3-loop order, i.e. third order in ε = 4 − d, where d is the internal dimension d. We also give the full 2-point function up to order ε 2 , i.e. at 2-loop order.arXiv:1707.09802v3 [cond-mat.dis-nn]
We calculate the effective action for disordered elastic manifolds in the ground state (equilibrium) up to 3-loop order. This yields the renormalization-group β-function to third order in ε = 4−d, in an expansion in the dimension d around the upper critical dimension d = 4. The calculations are performed using exact RG, and several other techniques, which allow us to resolve consistently the problems associated with the cusp of the renormalized disorder. arXiv:1801.08483v2 [cond-mat.dis-nn]
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