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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 us 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.
Fakher F. Assaad (Tue,) studied this question.