Symmetry-protected topological (SPT) phases are bulk-gapped quantum phases with symmetries, which have gapless or degenerate boundary states as long as the symmetries are not broken. The SPT phases in free fermion systems, such as topological insulators, have been experimentally discovered and classified; however, it is not known what SPT phases exist in general interacting systems. In this talk, I discuss a systematic way to construct SPT phases in interacting bosonic systems. Just as group theory allows us to construct 230 crystal structures in three-dimensional space, we use group cohomology theory to systematically construct different interacting bosonic SPT phases in any dimension and with any symmetry. We discover one bosonic topological insulator in two dimension, three kinds in three dimension and one bosonic topological superconductor in three dimension.
Dr. Xie Chen is a research fellow at Miller Institute for Basic Research in Science, University of California, Berkeley. She received her Bachelor’s degree from Tsinghua University in Physics in 2006. Then she went to MIT, where she became a PhD student of Prof. Xiao-Gang Wen and did excellent works on topological phases and quantum computation. She received her Ph.D degree in Physics in 2012.