Symmetry indicators for many-body topological phases

It is well known that many topological phases can be indicated by the symmetry behavior of their band structure at high symmetry points, which culminated in the development of topological quantum chemistry. This approach becomes problematic once interactions are added, as this does not permit conserved particle occupation numbers in reciprocal space. We face this challenge by generalizing the canonical momentum for translation invariant many-body wave functions via twisted boundary conditions. This allows for a symmetry analysis of the ground state wave function in twisted boundary space. We apply this ansatz to detect topological phase transitions in interacting Chern insulators and fractional Chern insulators by means of symmetry indicators.