Abstract
Entanglement only exists in quantum states and this can be viewed as the fundamental distinction between classical physics and quantum physics. As a non-local physical quantity, entanglement to some extent uncovers the veil of the fascinating properties of quantum world. In order to fulfill our desire to quantify the entanglement between a subsystem A with the rest of the system, the von-Neumann entropy has been introduced and fortunately its generalization the Rényi entropy (EE) can be measured by Monte Carlo (MC) methods, which gives us an efficient way of measuring the entanglement entropies in 2D or higher dimensions. Among all the available MC techniques of detecting EEs, one common trick is to take use of its trace structures to perform the measurement and various algorithms have been designed which gives many fascinating results. In this proposal, several efficient algorithms will be reviewed, including the replica partition functions trick and the non-equilibrium measurement of EE. In the end, a newly developed concept in conformal field theory called the disordered operator which is closely related to the 2nd Rényi entropy at Ising transitions is discussed. Hopefully this breakthrough will give more insights in the nature of quantum entanglement.
Reference:
- Humeniuk, S., & Roscilde, T. (2012). Quantum Monte Carlo calculation of entanglement Rényi entropies for generic quantum systems. Physical Review B, 86(23), https://doi.org/10.1103/physrevb.86.235116
- Laflorencie, N. (2016). Quantum entanglement in condensed matter systems. Physics Reports, 646, 1–59. https://doi.org/10.1016/j.physrep.2016.06.008
- Jiarui Zhao, Zheng Yan, Meng Cheng, and Zi Yang Meng, arXiv:2011.12543(2020). (PRR under review)
Anyone interested is welcome to attend.