  Entanglement measures such as the entanglement entropy have become an
indispensable tool to identify the fundamental character of ground states of
interacting quantum many-body systems. For systems of interacting spin or
bosonic degrees of freedom much recent progress has been made not only in the
analytical description of their respective entanglement entropies but also in
their numerical classification. Systems of interacting fermionic degrees of
freedom however have proved to be more difficult to control, in particular with
regard to the numerical understanding of their entanglement properties. Here we
report a generalization of the replica technique for the calculation of Renyi
entropies to the framework of determinantal Quantum Monte Carlo simulations --
the numerical method of choice for unbiased, large-scale simulations of
interacting fermionic systems. We demonstrate the strength of this approach
over a recent alternative proposal based on a decomposition in free fermion
Green's functions by studying the entanglement entropy of one-dimensional
Hubbard systems both at zero and finite temperatures.
