Response of Crystalline Symmetry Protected Topological Order to Symmetry Defects in the Presence of Interaction

We extend the previous study of extracting crystalline symmetry-protected topological invariants to the correlated regime. We construct the interacting Hofstadter Hamiltonian defined on the lattice with the rotation and translation symmetry defects: disclination and dislocation. Employing the density matrix renormalization group (DMRG) method, we calculate the excess charge around the defects. We found that the topological invariants remain quantized in both sides of the critical point while tuning the interaction. The topological quantity is extracted to great precision. This study shows that tensor network could be an efficient approach to study the system with symmetry defect.