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Numerical difficulties associated with computing matrix elements of operators between Hartree–Fock–Bogoliubov (HFB) wavefunctions have plagued the development of HFB-based many-body theories for decades. The problem arises from divisions by zero in the standard formulation of the nonorthogonal Wick’s theorem in the limit of vanishing HFB overlap. In this Communication, we present a robust formulation of Wick’s theorem that stays well-behaved regardless of whether the HFB states are orthogonal or not. This new formulation ensures cancellation between the zeros of the overlap and the poles of the Pfaffian, which appears naturally in fermionic systems. Our formula explicitly eliminates self-interaction, which otherwise causes additional numerical challenges. A computationally efficient version of our formalism enables robust symmetry-projected HFB calculations with the same computational cost as mean-field theories. Moreover, we avoid potentially diverging normalization factors by introducing a robust normalization procedure. The resulting formalism treats even and odd number of particles on equal footing and reduces to Hartree–Fock as a natural limit. As proof of concept, we present a numerically stable and accurate solution to a Jordan–Wigner-transformed Hamiltonian, whose singularities motivated the present work. Our robust formulation of Wick’s theorem is a most promising development for methods using quasiparticle vacuum states. 

Abstract While basaltic volcanism is dominant during rifting and continental breakup, felsic magmatism may be a significant component of some rift margins. During International Ocean Discovery Program (IODP) Expedition 396 on the continental margin of Norway, a graphite‐garnet‐cordierite bearing dacitic unit (the Mimir dacite) was recovered in two holes within early Eocene sediments on Mimir High (Site U1570), a marginal high on the Vøring Transform Margin. Here, we present a comprehensive textural, petrological, and geochemical study of the Mimir dacite in order to assess its origin and discuss the geodynamic implications. The major mineral phases (garnet, cordierite, quartz, plagioclase, alkali feldspar) are hosted in a fresh rhyolitic, vesicular, glassy matrix that is locally mingled with sediments. The major element chemistry of garnet and cordierite, the presence of zircon inclusions with inherited cores, and thermobarometric calculations all support an upper crustal metapelitic origin. While most magma‐rich margin models favor crustal anatexis in the lower crust, thermobarometric calculations performed here show that the Mimir dacite was produced at upper‐crustal depths (<5 kbar, 18 km depth) and high temperature (750–800°C) with up to 3 wt% water content. In situ U‐Pb analyses on zircon inclusions give a magmatic crystallization age of 54.6 ± 1.1 Ma, consistent with emplacement that post‐dates the Paleocene‐Eocene Thermal Maximum. Our results suggest that the opening of the Northeast Atlantic was associated with a phase of low‐pressure, high‐temperature crustal anatexis preceding the main phase of magmatism.