@misc{9242481,
  abstract     = {{Causality is a fundamental requirement for physical consistency in many-body approximations. In the context of Green's functions, causality requires a positive spectral function and analyticity in the upper half of the complex-frequency plane. These properties are not guaranteed by approximate methods, and formal proofs of causality for the underlying approximation schemes are often difficult to establish. The recently rediscovered Nevanlinna--Pick criterion provides a practical way to test causality directly from Matsubara-frequency data, without performing analytic continuation to the real-frequency axis. In this work, we use the Nevanlinna--Pick criterion to investigate the causality of the ladder dual-fermion approach, a diagrammatic extension of dynamical mean-field theory designed to incorporate nonlocal correlations. The analysis is performed for the spinless Falicov--Kimball model, which provides a useful testing ground because several quantities can be computed exactly or semi-analytically, avoiding Monte Carlo noise. This is particularly important since the Nevanlinna--Pick criterion is highly sensitive to noise in the input data. In addition, we derive several analytical properties of the Pick matrix, providing insight into the structure of the criterion when applied to Green's functions. For small systems, apparent causality violations are observed, but these are found to be associated with finite-size effects. For larger system sizes, no robust signs of causality violations are found, neither within the full ladder dual-fermion approach nor within the leading dual-fermion correction.}},
  author       = {{Skoglund, William}},
  language     = {{eng}},
  note         = {{Student Paper}},
  title        = {{Causality in the Dual-Fermion Approach}},
  year         = {{2026}},
}