Real-frequency quantum field theory applied to the single-impurity Anderson model
arxiv(2023)
摘要
A major challenge in the field of correlated electrons is the computation of
dynamical correlation functions. For comparisons with experiment, one is
interested in their real-frequency dependence. This is difficult to compute, as
imaginary-frequency data from the Matsubara formalism require analytic
continuation, a numerically ill-posed problem. Here, we apply quantum field
theory to the single-impurity Anderson model (AM), using the Keldysh instead of
the Matsubara formalism with direct access to the self-energy and dynamical
susceptibilities on the real-frequency axis. We present results from the
functional renormalization group (fRG) at one-loop level and from solving the
self-consistent parquet equations in the parquet approximation. In contrast to
previous Keldysh fRG works, we employ a parametrization of the four-point
vertex which captures its full dependence on three real-frequency arguments. We
compare our results to benchmark data obtained with the numerical
renormalization group and to second-order perturbation theory. We find that
capturing the full frequency dependence of the four-point vertex significantly
improves the fRG results compared to previous implementations, and that solving
the parquet equations yields the best agreement with the NRG benchmark data,
but is only feasible up to moderate interaction strengths. Our methodical
advances pave the way for treating more complicated models in the future.
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