# SNU Physics/IBS-CCES Distinguished Lecture Series [Mar.18– 21]

The SNU Physics and IBS-CCES will co-host Distinguished Lecture Series to provide the information on innovative research and fundamental physics knowledge to graduate students and researchers.

The second lecturer will be Prof. Masaki Oshikawa who is an expert in the theory for strongly correlated many-body systems, from Institute for Solid State Physics (ISSP), University of Tokyo, Japan.

Prof. Masaki Oshikawa has been a professor at ISSP, University of Tokyo since 2006, and also has been a senior scientist of Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU) since 2016. Prof. Oshikawa’s main research interest is “Field theoretical approach to strongly correlated quantum many body systems”. He made various important achievement in the theoretical study of strongly correlated many-body systems. Thus, the SNU Physics and IBS-CCES has decided to host Prof. Oshikawa as the second lecturer of the Distinguished Lecture Series. The lectures will cover the basics of many body physics as well as the result of latest research (see attached for detailed information).

We hope that this will be the valuable opportunity for graduate students and researchers.

Head of Department of Physics & Astronomy, Heonsu Jeon / Director of IBS-CCES, Tae Won Noh

SNU Physics/IBS-CCES Distinguished Lecture Series 2019.03.18.-21. (10am-12pm , 1:30pm–3:30pm) Seoul National University

“Field theoretical approach to strongly correlated quantum many body systems” by Prof. Masaki Oshikawa (ISSP, University of Tokyo)

Lecture I (03.18, Mon, Bldg. 25-1, International conference room) -Bosonization of 1D systems and Tomonaga-Luttinger Liquid -Bosonization approach to "Haldane gap" Lecture Video 18 PM

Lecture II (03. 19, Tue, Bldg. 25-1, International conference room) -Commensurability and Lieb-Schultz-Mattis theorem Lecture Video 19 AM -Bulk-boundary correspondence Lecture Video 19 PM

Lecture III (03. 20, Wed, Bldg. 500 Mokam Hall) -Chiral anomaly and condensed matter physics Lecture Video 20 AM -Polarization of quantum many-body systems Lecture Video 20 PM

Lecture IV (03.21, Thu, Bldg. 25-1, International conference room) -Anomaly and symmetry-protected topological phases Lecture Video 21 AM -Towards a systematic understanding of gapless critical phases Lecture Video 21 PM

(Detailed plan of lecture series is subject to change.) The abstract for the whole lecture series is as follows. While strongly correlated quantum many-body problems cannot be solved exactly in general, their universal behaviors in the low-energy limit are often described by field theory. I will illustrate this intriguing connection using quantum spin chains as an example. A wide range of quantum many-body systems in one spatial dimension, including quantum spin chains, can be mapped to a relativistic field theory of bosons, which is also known as Tomonaga-Luttinger Liquid (TLL) with possible perturbations. Following Haldane's original (and long-forgotten) argument, I will show that the difference in the possible perturbations to the TLL leads to the fascinating difference between integer and half-odd-integer spin quantum number, known as "Haldane conjecture". The difference can be understood as a consequence of Lieb-Schultz-Mattis theorem, which reflects the (in)commensurability of the particle number with the periodic lattice structure. The Lieb-Schultz-Mattis theorem for the lattice model implies an "anomaly" of the corresponding field theory. While these connections would be most clearly understood in one spatial dimension, they have been extended to higher dimensions. I will discuss extensions of Lieb-Schultz-Mattis theorem in higher dimensions and its implications on field theory, and more generally the relevance of anomaly in field theories to condensed matter physics.