| Brief Bio of the Speaker | Chen Fang graduated from Purdue University with a PhD degree in physics in 2011. He worked as a postdoctoral research associate at Princeton University, University of Illinois, and Massachusetts Institute of Technology from 2011 to 2015. He joined the faculty of Institute of Physics, Chinese Academy of Sciences in 2015 as an associate professor, and was promoted to professor in 2018. Chen Fang has led his team to create, among other two international teams, the research field of high-order topological states in 2017. The same team in 2018 established the quantitative mappings between symmetry representations of bands and topological invariants, based on which he and Hongming Weng founded the Catalogue of Topological Electronic Materials in 2019. Since 2019, Chen Fang started to explore new research directions such as the bulk-edge correspondence in non-hermitian systems, and the quantum-many-body-scar dynamics. |
Abstract | I demonstrate a link between two phenomena in non-hermitian systems: the phase winding of the eigenvalue of the non-hermitian Hamiltonian on the complex plane under periodic-boundary condition, and the Non-hermitian-skin effect under open-boundary condition. The latter means the presence of an extensive number of localized modes, termed skin modes, at the boundaries, an effect that is restricted to non-hermitian systems. This link is established as a theorem in 1D for one-band Hamiltonians, and as a conjecture in higher dimensions and in multi-band cases. Moreover, we develop an effective numerical method to solve for the open-boundary eigenvalues of any 1D non-hermitian Hamiltonian in the thermodynamic limit, by converting the problem into solving a set of algebraic equations. References: [1] K. Zhang, Z. Yang, and C. Fang*, Phys. Rev. Lett. 125, 126402 (2020) [2] Z. Yang, K. Zhang, C. Fang* and J. Hu*, arXiv:1912.05499 (to appear in Phys. Rev. Lett.)
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