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 Rényi negativity 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 one- and two-dimensional systems, ground and thermal states, and bipartite and tripartite partitions, not only is the information of the underlying conformal field theory achieved, but the role of entanglement in quantum and thermal phase transitions is revealed.

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• Critical phenomena
• Phase transitions
• Quantum entanglement
• Quantum many-body systems
• Strongly correlated systems
• Quantum Monte Carlo