Entanglement dynamics from random product states at long times (Sep. 27, 2021)

  • Published: 2021-09-23

Time: 10:00am (UTC/GMT+8:00, Beijing/Shanghai), Sep. 27 (Mon.), 2021

Zoom URL: https://us06web.zoom.us/j/86487268813

Meeting ID: 864 8726 8813


Speaker: Huang Yichen (MIT)



We study the entanglement dynamics of quantum many-body systems at long times.

For upper bounds, we prove the following: (I) For any geometrically local Hamiltonian on a lattice, starting from a random product state the entanglement entropy almost never approaches the Page curve. (II) In a spin-glass model with random all-to-all interactions, starting from any product state the average entanglement entropy does not approach the Page curve. We also extend these results to any unitary evolution with charge conservation and to the Sachdev-Ye-Kitaev model.

For lower bounds, we say that a Hamiltonian is an ``extensive entropy generator'' if starting from a random product state the entanglement entropy obeys a volume law at long times with overwhelming probability. We prove that (i) any Hamiltonian whose spectrum has non-degenerate gaps is an extensive entropy generator; (ii) in the space of (geometrically) local Hamiltonians, the non-degenerate gap condition is satisfied almost everywhere. These results imply ``unbounded growth of entanglement’’ in many-body localized systems.

References: arXiv:2102.07584 & 2104.02053


About the Speaker:

Yichen Huang received the B.Sc. degree in Mathematics and Physics from Tsinghua University in 2010 and the Ph.D. degree in Physics from the University of California, Berkeley in 2015. He was an IQIM Postdoctoral Scholar at the California Institute of Technology from 2015 to 2018 and an Associate Researcher at Microsoft Research AI from 2018 to 2019. Since 2019, he has been a Senior Postdoctoral Associate at the Center for Theoretical Physics, Massachusetts Institute of Technology. His research interest includes condensed matter theory, quantum information theory, and natural language processing.