  Many-body entanglement unveils additional aspects of quantum matter and
offers insights into strongly correlated physics. While ground-state
entanglement has received much attention in the past decade, the study of
mixed-state quantum entanglement using negativity in interacting fermionic
systems remains largely unexplored. We demonstrate that the partially
transposed density matrix of interacting fermions, similar to their reduced
density matrix, can be expressed as a weighted sum of Gaussian states
describing free fermions, enabling the calculation of rank-$n$ R\'{e}nyi
negativity within the determinant quantum Monte Carlo framework. We conduct the
first calculation of the rank-two R\'{e}nyi negativity for the half-filled
Hubbard model and the spinless $t$-$V$ model. Our calculation reveals that the
area law coefficient of the R\'{e}nyi negativity for the spinless $t$-$V$ model
has a logarithmic finite-size scaling at the finite-temperature transition
point. Our work contributes to the calculation of entanglement and sets the
stage for future studies on quantum entanglement in various fermionic many-body
mixed states.
