ABSTRACT
Since the seminal work by P. W. Anderson in 1958 [1], quantum localization has been a central subject of condensed matter physics. In the past decade, this subject has again become an area of intense research activities as people realized that (single-particle) Anderson localization may survive finite interactions [2], leading to a many-body localized phase. More importantly, when an isolated system is many-body localized, it strongly violates the familiar ergodicity hypothesis in quantum statistical mechanics, and fails to thermalize on its own. In this talk I will focus on a one-dimensional mutually incommensurate bichromatic lattice system which has been implemented in ultra-cold atoms to study quantum localization. We argue that without interactions, there exists a single-particle mobility edge (SPME) in the energy spectrum [3], which is an energy that separates extended eigenstates from localized ones. Our theoretical work subsequently led to a first experimental observation of SPME in one-dimensional systems [4-5]. We further study the properties of many-body localization in such a system when the interaction is turned on, and discuss its implications for a possible many-body mobility edge. In particular, we show that state-of-theart machine learning techniques can help us understand the phase diagram in this intriguing many-body system.
References:
[1] P. W. Anderson, Phys. Rev. 109, 1492 (1958).
[2] D. M. Basko, I. L. Aleiner, and B. L. Altshuler, Ann. Phys. 321, 1126 (2006).
[3] Xiao Li, Xiaopeng Li, and S. Das Sarma, Phys. Rev. B 96, 085119 (2017).
[4] H. Luschen et al., arXiv: 1709.03478, to appear in PRL.
[5] T. Kohlert, et al., to be submitted.
BIOGRAPHY
Dr. Xiao Li received his Bachelor’s degree from Peking University in 2008, and his PhD in 2014 under the guidance of Dr. Qian Niu from The University of Texas at Austin. He is currently a Postdoctoral Fellow working with Dr. S. Das Sarma at the Condensed Matter Theory Center, University of Maryland, College Park. Dr. Li is primarily interested in novel topological phases in low-dimensional systems, and many-body localization.