Special Seminar - Non-Bloch band theory in arbitrary dimensions: the stable and the fragile - Jadwin A09 - 2 PM

Dec 11, 2023, 2:00 pm3:00 pm
Jadwin Hall A09
Faculty, post docs, grads



Event Description

The non-Hermitian skin effect (NHSE) is a phenomenon that occurs in non-Hermitian lattice systems, in which eigenstates are massively squeezed to the boundary. In our recent works, we propose a universal solution to the NHSE under open boundary condition in any spatial dimensions (arXiv: 2212.11743), borrowing the concept of amoeba from algebraic geometry. With the amoeba formulation, we can determine many key spectral features, including the density of states, eigenstate profiles, and the generalized Brillouin zone. We show that the “amoebic spectrum” is the unique stable eigenvalue spectrum against disorder. On the other hand, there are known cases that the spectrum can deviate from the amoebic spectrum, and their mechanisms are not fully revealed. We found that a good indicator of the appearance of NHSE is the singular value zero mode, which is universal enough to explain both the stable and the non-stable spectra. Also, this point of view unequivocally relates NHSE to certain kind of winding topology. Finally, we address a potential usage of the unstable spectra in terms of the Green’s function.