Arguably one of the central pieces in solid state physics is band structure theory. This provides an interpretable formalism to rationalize and predict the behavior of electrons in periodic systems in terms of effective, non-interacting models. Thanks to efficient computational frameworks leveraging band structures, particularly Kohn-Sham density functional approximations, theory plays an important role in the exploration and design of functional materials. Unfortunately, the situation is more challenging when it comes to leveraging strongly correlated electrons. Their immense potential for device design is fundamentally more difficult to chart, as theoretical and computational models for them traditionally need to abandon the band structure picture.

Among these approaches, the ghost Gutzwiller (gGut) framework has recently emerged as a versatile alternative to well established, computationally intensive methods. gGut is a variational Ansatz which can be formulated as a local embedding. Crucially, by introducing auxiliary orbitals, it can describe correlated electrons in lattices and molecules in terms of effectively non-interacting quasiparticles, recovering a band structure picture valid for strong correlation. Here, we will discuss two recent gGut applications: the proposal of an interaction-driven mechanism for altermagnetism and the description of topological properties in correlated materials. In the former, the interplay between van Hove itinerant magnetism and local exchange interactions leads to a homogeneous altermagnetic spin ordering. In the latter, the quasiparticle picture underlying gGut allows the immediate use of markers developed for non-interacting systems to describe correlated topology. These examples show how gGut can provide transparent descriptions of correlated phenomena in terms of non-interacting quasiparticles.