Exceptional bound states represent a unique class of robust bound states protected by the defectiveness of non-Hermitian exceptional points. Conceptually distinct from the more well-known topological and non-Hermitian skin states, they were recently discovered [1] as a novel source of negative entanglement entropy in the quantum entanglement context, generalizing the previous observation by Ryu et. al [2]. They arise as enigmatic negative probability eigenstates in the free-fermion propagator, and exhibit an interesting spectral flow as the entanglement cut is moved, reminiscent to but distinct from the spectral flow of topological states. In this talk, I shall explain how to realize exceptional bound states in the Hamiltonians or network Laplacians of classical systems, and describe their first experimental observation in an electrical circuit. Surprisingly, exceptional bound states they remain extremely robust in small local lattice networks, despite their mathematical origin in highly non-local propagators. From a broader perspective, I shall also describe how exceptional bound phenomena can interplay with topology and/or the critical non-Hermitian skin effect to yield new classes of robust hybrid states.

1. [1] Lee, Ching Hua. "Exceptional bound states and negative entanglement entropy." Physical Review Letters 128.1 (2022): 010402.
2. [2] Chang, Po-Yao, Jhih-Shih You, Xueda Wen, and Shinsei Ryu. "Entanglement spectrum and entropy in topological non-Hermitian systems and nonunitary conformal field theory." Physical Review Research 2, no. 3 (2020): 033069.