Moving beyond mean-field band structure theory: natural orbital representation of electronic correlations, topology and dynamics
Mean-field energy bands and their Bloch functions have long served as a starting point for understanding the electronic structure of solids, yet this picture can be qualitatively wrong in correlated materials such as Mott insulators. While symmetry breaking sometimes saves the mean-field picture, it is always possible to define a band structure that respects the symmetries of the system by starting from the wave function itself.
The eigenfunctions and eigenvalues of the one-body reduced density matrix define so-called natural Bloch orbitals and occupation number bands without the need to invoke an auxiliary single-particle Hamiltonian. I will describe some examples where this natural orbital band structure concept has been useful, including calculations of the many-body macroscopic polarization, topological phase diagrams, and real-time dynamics in interacting lattice models.