Abstract: Many-body localization (MBL) is a dynamical phenomenon occurring in isolated many-body quantum systems with strong disorder. It is characterized by the system failing to reach thermal equilibrium, and retaining a memory of its initial condition in local observables for infinite time. Theoretically, MBL systems exhibit a new kind of robust integrability: an extensive set of quasilocal integrals of motion emerges, which provides an intuitive explanation of the breakdown of thermalization.

In this talk, I will start with an introduction to thermalization in quantum systems. The eigenstate thermalization hypothesis (ETH) will be mentioned. Then I will focus on MBL systems which fail to thermalize. A description based on quasilocal integrals of motion is used to predict dynamical properties of MBL systems, such as the spreading of quantum entanglement and the behavior of local observables. The delocalization transition will be discussed next. Here I will mainly talk about transition diagnostics related to entanglement spectrum. At last, I will talk about experiments of MBL with ultracold atoms.

References:

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[3] Z-C Yang, C. Chamon, A. Hamma, and E. R. Mucciolo, Two-Component Structure in the Entanglement Spectrum of Highly Excited States, Phys. Rev. Lett. 115, 267206 (2015).

[4] A. Samanta, K. Damle, and R. Sensarma, Tracking the many-body localized to ergodic transition via extremal statistics of entanglement eigenvalues, Phys. Rev. B 102, 104201 (2020).