Entanglement Renyi 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 unexplored. We demonstrate that the partially transposed density matrix of interacting fermions, similar to the reduced density matrix, can be expressed as a weighted sum of Gaussian states describing free fermions, enabling the calculation of rank-n Re ́nyi negativity within the determinantal quantum Monte Carlo framework. We conduct the first calculation of rank-two Renyi negativity for the half-filled Hubbard model and the spinless t-V model and find that the area law coefficient of the Renyi negativity has a singularity 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.