  We show that the two recently proposed methods to compute Renyi entanglement
entropies in the realm of determinant quantum Monte Carlo methods for fermions
are in principle equivalent, but differ in sampling strategies. The analogy
allows to formulate a numerically stable calculation of the entanglement
spectrum at strong coupling. We demonstrate the approach by studying static and
dynamical properties of the entanglement hamiltonian across the interaction
driven quantum phase transition between a topological insulator and quantum
antiferromagnet in the Kane-Mele Hubbard model. The formulation is not limited
to fermion systems and can readily be adapted to world-line based simulations
of bosonic systems.
