学术会议（12月10日）

主持人：张笑教授

欢迎广大师生踊跃参加！

摘要：

Fractionalization in condensed matter has been associated with a diverse range of interesting topological states from the Laughlin states to more exotic states like the Pfaffian, Haffnian, Gaffnian, Read-Rezayi states and so on. Many fractional quantum Hall wavefunctions are known to be unique highest-density zero modes of certain positive-definite operators known as “pseudopotential” Hamiltonians. While a systematic method to construct such parent Hamiltonians has been available for the infinite plane and sphere geometries, the generalization to manifolds where relative angular momentum is not an exact quantum number, i.e., the cylinder or torus, remains an open problem. This is particularly true for non-Abelian states, such as the Read-Rezayi series, as well as more exotic nonunitary (Haldane-Rezayi and Gaffnian) or irrational (Haffnian) states, whose parent Hamiltonians involve complicated many-body interactions. I shall discuss an universal geometric approach for constructing pseudopotential Hamiltonians that is applicable to all geometries, and which even generalizes to systems with internal degrees of freedom i.e. spin or pseudospin (layer, subband, or valley). This approach can be analyzed transparently through root configurations in the Tao-Thouless limit, where the construction of the fusion algebra (modular tensor category) for the quasiparticles becomes a (relatively) simple exercise in combinatorics.

报告人简介：

Dr. Ching Hua Lee is currently a Research Scientist at Singapore Institute of High Performance Computing. He received his PhD at Stanford University. He research interests include N=8 super Yang-Mills theory, topological insulators, multicomponent fractional quantum hall systems, holography, complex networks and decision-making.