Tracking the variation of entanglement R\'enyi negativity: a quantum Monte Carlo study

Entanglement entropy has been a powerful tool for analyzing phases and criticality in pure ground states via quantum Monte Carlo (QMC). However, mixed-state entanglement, relevant to systems with dissipation, finite temperature, and disjoint regions, remains less explored due to the lack of efficient numerical methods. In this work, we present a practical and easy-to-implement QMC method within the reweight-annealing framework, enabling efficient computation of the entanglement R\'enyi negativity (RN) by tracking its variation along given parameter paths. This method is scalable, parallelizable, and well-suited for high-dimensional and large-scale simulations. Applying it to diverse scenarios-including 1D and 2D systems, ground and thermal states, and bipartite and tripartite partitions, not only the information of the underlying conformal field theory is achieved, but the role of entanglement in quantum and thermal phase transitions is revealed.