1. krylov complexity of many-body localization: operator localization in the krylov basis

Cheng-Ju Lin

Perimeter Institute, Canada

18 January 2022 Tue 4 pm

                                      IBS Center for Theoretical Physics of Complex Systems (PCS), Administrative Office (B349), Theory Wing, 3rd floor

                                      Expo-ro 55, Yuseong-gu, Daejeon, South Korea, 34126 Tel: +82-42-878-8633                     

Motivated by the recent developments of quantum many-body chaos, characterizing how a operator grows and its complexity in the Heisenberg picture has attracted a lot of attentions. In this talk, I will discuss the operator growth problem in a many-body localization (MBL) system from a recently proposed Lanczos algorithm perspective. Using the Krylov basis, the operator growth problem can be viewed as a single-particle hopping problem on a semi-infinite chain with the hopping amplitudes given by the Lanczos coefficients.  We find that, in MBL, the asymptotic behavior of the Lanczos coefficients is the same as in the ergodic phase.  However, the Lanczos coefficients in MBL have an additional even-odd alteration and effective randomness. We show numerical evidence that the corresponding single-particle problem is localized, resulting in a bounded “Krylov complexity” in time, in contrast to the exponential growth of “Krylov complexity” in time in the ergodic phase. We also study the “Krylov complexity” in the MBL phenomenological model, and found that the Krylov complexity grows linearly in time.