Speaker: Masaki Tezuka (Kyoto Univ.)

Date: Jan. 25th, 17:30-

Style: Webinar

Title: Many-body localization, ergodicity and operator scrambling

Abstract: Many-body localization (MBL) has been extensively studied in the last two or more decades, however, strong consensus has not been reached on such questions as whether the MBL phase is stable in the thermodynamic limit (especially in short-range interacting systems in d>1 spatial dimensions), and whether there is an intermediate phase between the thermal phase and MBL. Confined many-body systems with long-range interactions, such as the Sachdev-Ye-Kitaev model with a random one-body term [1], permit more analytic approaches on such questions [2]. Here we discuss the distribution of eigenstate wave functions outside the localized regime. We argue that in the delocalized phase eigenstates are ergodic and thermally extended over their energy shell, which has a non-trivial, correlated structure in the Fock space and whose volume decreases as the disorder is increased. For a variant of the Sachdev-Ye-Kitaev model, we find that the numerically obtained entanglement entropy agrees with our analytical prediction [3]. We also discuss the time evolution of bi- and tripartite operator mutual information, which is the entanglement structure of operators rather than wave functions, in and outside the MBL regime in the short-range Heisenberg model with a random magnetic field [4].

[1] see e.g. A. M. García-García, B. Loureiro, A. Romero-Bermúdez, and M. Tezuka, Phys. Rev. Lett. 120, 241603 (2018) [arXiv:1707.02197; see also 2007.06121].

[2] F. Monteiro, T. Micklitz, M. Tezuka, and A. Altland, Phys. Rev. Research 3, 013023 (2021) [arXiv:2005.12809].

[3] F. Monteiro, M. Tezuka, A. Altland, D. A. Huse, and T. Micklitz, arXiv:2012.07884.

[4] E. Mascot, M. Nozaki, and M. Tezuka, arXiv:2012.14609.