【直播】【复旦理论物理报告会】中科院物理所胡海平研究员：Knot theory of non-Hermitian ……

直播信息

报告题目

Knot theory of non-Hermitian bands and exceptional points

报告人

胡海平 研究员（中国科学院物理所）

报告时间

2022年4月30日（周六）09:30

主办方

复旦大学物理系

直播二维码

报告人介绍

胡海平，中国科学院物理研究所“百人特聘研究员”，博士生导师。2011年9月毕业于中国科学技术大学零零班。2016年7月在中国科学院物理研究所获得物理博士学位。2016年9月-2021年9月分别在德州大学达拉斯分校，匹兹堡大学和乔治梅森大学从事博士后研究。2021年9月加入中国科学院物理研究所。主要研究方向为拓扑凝聚态理论，量子动力学，原子分子与光物理和量子模拟理论。

报告摘要

Non-Hermitian (NH) physics has emerged as an interdisciplinary research area during the past several years, fueled by the explosive theoretical/experimental explorations of NH Hamiltonian and exceptional point (EP) across a diverse set of photonic platforms with gain/loss, cold-atom systems, metamaterials, and condensed matter materials. Here we provide a systematical classification of NH bands and EPs using homotopy theory. We show that knots tied by the eigenenergy strings provide a complete topological classification of 1D NH Hamiltonians with separable bands. The transition between two phases characterized by distinct knots occurs through EPs and comes in two types. EPs are peculiar band degeneracies in non-Hermitian systems with broad physical applications. We demonstrate that an n-th order EP in 2D is fully characterized by the braid group, with its eigenenergies tied up into a geometric knot along a closed path enclosing the EP. The quantized discriminant invariant of the EP is the writhe of the knot. The knot crossing number gives the number of bulk Fermi arcs emanating from each EP. We put forward a no-go theorem, which governs the possible configurations of EPs and their splitting rules on a 2D periodic lattice and goes beyond the previous fermion doubling theorem. Our framework bridging the NH physics, algebraic topology, and knot theory opens a broad avenue for investigating the enigmatic properties of NH systems.

Reference

1. H. Hu and E. Zhao, Knots and non-Hermitian Bloch bands, Physical Review Letters 126 (1), 010401 (2021).2. H. Hu, S. Sun, and S. Chen, Knot Topology of Exceptional Point and Non-Hermitian No-Go Theorem, arXiv:2111.11346.

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