Towards a Topological Quantum Chemistry description of strongly correlated systems: the case of the Hubbard diamond chain

The recently introduced Topological Quantum Chemistry (TQC) formalism provides a description of the universal global properties of all possible atomic limit band structures in all groups, in real and momentum space. Using TQC, an algorithm interfaced with ab initio codes was developed, which allowed for high-throughput calculations on material databases identifying thousands of materials displaying topological properties at the Fermi level. However, it is an open question to which extent this formalism can be generalized to correlated systems that can exhibit symmetry protected topological phases which are not adiabatically connected to any band insulator. We address this question by considering the Hubbard diamond chain and apply TQC, together with the concept of topological Hamiltonian and Cluster Perturbation Theory, to study the different topological phases that this system exhibits and the phase transitions between them. We will compare our results with more sophisticated numerical methods.