Conserved quantities of SU(2)-invariant interactions for correlated fermions and the advantages for quantum Monte Carlo simulations

In the context of realistic calculations for strongly correlated materials with d or f electrons the efficient computation of multi-orbital models is of paramount importance. Here we introduce a set of invariants for the SU(2)-symmetric Kanamori Hamiltonian, which allows us to massively speed up the calculation of the fermionic trace in hybridization-expansion continuous-time quantum Monte Carlo algorithms. We show that by exploiting this set of good quantum numbers the study of the orbital-selective Mott transition in systems with up to seven correlated orbitals becomes feasible.