Abstract

Strong correlation in solids and molecules gives rise to a wide palette of states with highly tuneable electronic properties, ranging from Mott insulators and unconventional superconductors all the way to efficient and selective catalytic centres. Such systems share a common underlying motif: their unique phases emerge from the competition between different energy scales. Describing such competition can be achieved within an embedding framework, which entails identifying a small fragment of the system, modelled explicitly, while all the rest is substituted by some auxiliary, often frequency-dependent potential. Still, most embedding approaches suffer either from a limited access to observables or high computational cost. In this talk, I will discuss the type of information that an embedding analysis can provide for complex lattice systems. Moreover, I will present a powerful embedding framework recently introduced, which enhances the Gutzwiller Ansatz with auxiliary states. Dynamical correlators within this method are described in terms of an effective non-interacting, quasiparticle Hamiltonian, subject to a self-consistency condition formulated in terms of the one-particle reduced density matrix. Despite this comparatively simple, frequency-independent construction, I will show that this approach can generate qualitatively correct expectation values and spectral functions in multi-orbital models. This technique alleviates the flexibility vs cost trade-off, and is hence attractive for future applications in correlated solids and molecules, particularly when the coupling between fragment and environment plays a decisive role.