Wu Kai-Hsin, Lu Tsung-Cheng, Chung Chia-Min, Kao Ying-Jer, Grover Tarun
Department of Physics and Center of Theoretical Sciences, National Taiwan University, Taipei 10607, Taiwan.
Department of Physics, University of California at San Diego, La Jolla, California 92093, USA.
Phys Rev Lett. 2020 Oct 2;125(14):140603. doi: 10.1103/PhysRevLett.125.140603.
Quantum 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.
量子纠缠对热涨落很敏感，这就引出了一个问题：有限温度下的相变是否支持类似于零温度对应物的长程纠缠。在这里，我们使用量子蒙特卡罗模拟来研究三阶Rényi负性（纠缠负性的一种推广），作为二维横场伊辛模型在有限温度相变过程中混合态纠缠的一个代理。我们发现，Rényi负性的面积律系数在相变处是奇异的，而在统计误差范围内其次要常数为零。这表明，尽管关联长度发散，但在临界点处纠缠是短程的。几个精确可解模型中的Rényi负性也与二维横场伊辛模型中的Rényi负性表现出定性的相似性。
