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Nonperturbative effects of short-range spatial correlations at the two-particle level

Michael Meixner1,*, Matthias Reitner2,*, Thomas Schäfer1,3,†, and Alessandro Toschi2

  • *These authors contributed equally to this work.
  • †Contact author: t.schaefer@fkf.mpg.de
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Phys. Rev. Research 8, 033093 – Published 23 July, 2026

DOI: https://doi.org/10.1103/bqs7-k89d

Abstract

By means of cellular dynamical mean-field theory (CDMFT), we study how short-range correlations drive the breakdown of the self-consistent perturbation theory in two-dimensional systems and the most relevant physical consequences associated with it, such as the CDMFT Mott transition. To this aim, we first derive in a structured and consistent way the Bethe-Salpeter equation (BSE) formalism at the CDMFT level in all physical channels, explicitly addressing the important aspect of the related Ward identities. In this context, we perform systematic calculations of the BSE for the two-dimensional Hubbard model at half filling at intermediate coupling. Our study illustrates how the divergence of a fundamental building block of the BSE in the charge channel, the two-particle irreducible vertex, systematically occurs at lower interactions than in the (purely local) DMFT case. We establish that these divergences are a prerequisite for the CDMFT Mott instability in two dimensions, which occurs at larger interaction values, and explicitly demonstrate that both are driven by short-ranged antiferromagnetic spin fluctuations.

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Phys. Rev. Research 8, 033093– Published 23 July, 2026
  • Received 14 January 2026
  • Accepted 2 July 2026
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