Recent years have witnessed tremendous progress in the theoretical understanding of quantum matter beyond the Landau paradigm. The interplay of symmetry and entanglement structure of many-body wave functions results in new phases of matter exhibiting a variety of novel topological phenomena, such as fractionalization and quantized transport. I will discuss in particular a class of gapped phases known as symmetry-protected topological (SPT) phases, summarizing recent progress in their classifications. Contemplating the bulk-boundary relations for SPT phases has led to a deeper understanding of quantum anomalies and their implications for low-energy physics. I will explain how these ideas can be applied to condensed matter systems with crystalline symmetry, yielding vast generalizations and refinements of the celebrated Lieb-Schultz-Mattis theorem in quantum magnetism.
Prof Meng Cheng is an Assistant Professor of Physics at Yale University. He received his undergraduate degree from Nanjing University (China). In 2013, he obtained his Ph.D degree from the University of Maryland, College Park, where he studied topological superconductivity and its applications in quantum information processing. He then moved to a postdoctoral researcher position in Microsoft Research, Station Q in Santa Barbara, during which he investigated the interplay of global symmetry and topological quantum order. He joint the Department of Physics at Yale University in 2016.
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