Algorithmic inversion on sum over poles to embed interacting many-body systems

Quantum embedding methods are powerful techniques to study interacting correlated electrons beyond mean-field theories. An established approach is dynamical mean-field theory (DMFT), which tackles the problem by mapping strongly correlated electrons into an Anderson impurity model. Here, we start from a different approach meant to solve Dyson-like equations – the algorithmic inversion on sum over poles [1] – to provide an embedding formulation valid at zero or finite temperature and based on exact diagonalization. We demonstrate the approach on the one-dimensional Hubbard ring, performing self-consistent calculations on the real axis, ensuring the accurate computation of both spectral and thermodynamic quantities.

[1] T. Chiarotti, A. Ferretti, and N. Marzari, Phys. Rev. Research 6, L032023 (2024)