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In this talk, I will review our recent efforts towards a classification of fermionic crystalline-symmetry-protected topological states, which are based on two approaches. First, using the crystalline equivalence principle proposed by Thorngren and Else, the classification can be computed by treating the crystalline symmetries as onsite symmetries. We develop an algorithm that allows a fast computation of such classification for complex symmetry groups, including the space groups. Second, we use a real-space construction to build crystalline SPT states from lower-dimensional building blocks, which are topological states protected by onsite symmetries. I will discuss the progress and difficulties we are facing in each approach.
戚扬研究员2005年本科毕业于清华大学物理系，2010年于美国哈佛大学物理系获博士学位，导师为Sachdev教授。2010年至2014年在清华大学高等研究院任副研究员；2014年至2016年在加拿大理论物理圆周研究所访问；2016年至2017年在美国麻省理工学院物理系傅亮教授课题组做博士后。2017年11月起加入复旦大学任研究员。戚扬近年来的主要研究方向为强关联量子多体系统的理论研究，包括拓扑物态的分类、阻挫磁性系统和量子自旋液体、高温超导理论等。截止目前在包括Nature Communications, PRX, PRL, PRB等国际学术期刊上发表论文40余篇。