Entanglement R\'{e}nyi Negativity of Interacting Fermions from Quantum Monte Carlo Simulations

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 calculate 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.