Towards a topological quantum chemistry description of correlated systems: The case of the Hubbard diamond chain

The recently introduced topological quantum chemistry (TQC) framework has provided a description of universal properties all possible band insulators in space groups based on crystalline unitary symmetries and time reversal. While this formalism filled the gap between mathematical classification practical diagnosis materials, an obvious limitation is that it only applies to weakly interacting systems-which can be described within theory. It open question which extent generalized correlated systems exhibit symmetry protected phases are not adiabatically connected any insulator. In work we address many facettes by considering specific example Hubbard diamond chain. This model features Mott insulator, trivial insulating phase obstructed atomic limit phase. Here discuss nature insulator determine diagram topology with infinite density matrix renormalization group calculations, variational Monte Carlo simulations many-body invariants. We then proceed generalization TQC Green's functions combined concept Hamiltonian identify phases, using cluster perturbation theory calculate functions. results benchmarked above determined applicability limitations approach its extensions.