Wu K.-H., Lu T.-C., Chung C.-M., Kao Y.-J., Grover T.Lu T.-C., Chung C.-M., Kao Y.-J., Grover T.Wu K.-H.YING-JER KAO2021-07-282021-07-282020319007https://www.scopus.com/inward/record.uri?eid=2-s2.0-85093365616&doi=10.1103%2fPhysRevLett.125.140603&partnerID=40&md5=f97297379d66070cce549942d002411bhttps://scholars.lib.ntu.edu.tw/handle/123456789/575271Quantum entanglement is fragile to thermal fluctuations, which raises the question whether finite temperature phase transitions support long-range entanglement similar to their zero temperature counterparts. Here we use quantum Monte Carlo simulations to study the third Renyi negativity, a generalization of entanglement negativity, as a proxy of mixed-state entanglement in the 2D transverse field Ising model across its finite temperature phase transition. We find that the area-law coefficient of the Renyi negativity is singular across the transition, while its subleading constant is zero within the statistical error. This indicates that the entanglement is short-range at the critical point despite a divergent correlation length. Renyi negativity in several exactly solvable models also shows qualitative similarities to that in the 2D transverse field Ising model. ? 2020 American Physical Society.Ising model; Monte Carlo methods; Correlation lengths; Exactly solvable model; Finite temperatures; Finite-temperature transition; Quantum Monte Carlo simulations; Statistical errors; Thermal fluctuations; Transverse-field Ising model; Quantum entanglement; article; Monte Carlo method; phase transitionjournal article10.1103/PhysRevLett.125.140603330645322-s2.0-85093365616