Direct minimization versus iterative embedding in the ghost-Gutzwiller method: a comparative study of magnetism in Mott insulators
arXiv:2607.27156
The paper compares two ways of solving the ghost‑Gutzwiller method—iterative embedding and direct energy minimization—showing that the iterative approach is efficient but can fail in the paramagnetic Mott phase, while direct minimization remains stable, and that both methods agree for antiferromagnetic order.
Abstract
Accurately describing a hypothetical symmetry-invariant Mott insulator presents a long-standing ing challenge in iterative quantum embedding methods. We address this issue within the ghost- Gutzwiller method, which can be solved either through an iterative embedding scheme, analogous to dynamical mean-field theory, or by directly minimizing its variational energy functional. Across the Mott transition of the single-band Hubbard model, these formally equivalent approaches behave very differently: the iterative scheme is computationally efficient but fragile, necessitating ad-hoc recipes in the Mott phase that fail in a Zeeman field, leading to a discontinuous energy and a spurious fully-polarized insulator. Direct minimization avoids these artifacts, stabilizing a genuinely paramagnetic solution. Conversely, when symmetry breaking is allowed, as in an antiferromagnetic phase, the iterative scheme yields the correct solution, closely aligning with dynamical mean-field theory. Our findings delineate the conditions under which the iterative embedding can be trusted and when direct minimization is instead required.