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Understanding quantum statistical mechanics in an isolated system and how machine learning can help

September 10, 2018 - 11:30am
Xiao Li
Since the seminal work by P. W. Anderson in 1958 [1], quantum localization in a disordered system 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 even in the presence of interactions, a many-body system can generally fail to thermalize on its own when strong disorder is present, leading to a stable dynamical phase of matter at non-zero temperatures [2]. Such a perfect interacting insulator has since been termed as many-body localized (MBL). More importantly, an MBL system strongly violates the familiar ergodicity hypothesis in quantum statistical mechanics, so that many of our intuitions from equilibrium systems no longer apply. In this talk, I will focus on a one-dimensional mutually incommensurate bichromatic lattice system which has been implemented in ultracold 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 has led to the first experimental observation of SPME in one-dimensional systems [4]. 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 intermediate phase [5]. In particular, we show that state-of-the-art machine learning techniques [6] can help us understand the phase diagram in this intriguing many-body system. 
[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., Phys. Rev. Lett. 120, 160404 (2018). 
[5] T. Kohlert, et al., to be submitted. 
[6] Y.-T. Hsu, Xiao Li, D.-L. Deng, and S. Das Sarma, arXiv:1805.12138 (2018).
ATL 2400