Direct minimization versus iterative embedding in the ghost-Gutzwiller method: a comparative study of magnetism in Mott insulators

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.