Higher-order exceptional points of many-body unidirectional Hatano-Nelson model
Shunta Kitahama (Tokyo University)
We study higher-order exceptional points (EP) of the unidirectional Hatano-Nelson model, which is one of the simplest non-Hermitian models.
In the first part, we introduce the procedure to obtain the Jordan decomposition of the unidirectional Hatano-Nelson model [1]. By identifying the Hamiltonian with one of the generators of sl₂ algebra, it is proved that the Jordan decomposition is obtained from polynomials called q-binomial coefficients.
In the second part, we investigate two physical properties of the unidirectional Hatano-Nelson model caused by higher-order EP structure: perturbations and dynamics. First, we focused on enhanced sensitivity of EP to perturbations. The energy level splitting due to perturbations around an n-th order EP exhibits 1/n-th power of the parameters [2]. By introducing a certain perturbation to the EP, we were able to observe the level splitting expected from the Jordan decomposition calculated in [1]. Second, we focused on the dynamics of observables. The dynamics at EPs shows polynomial behavior over time. We calculated the particle number at each site as an observable. As a result, we found power law dynamics in short time and long time dynamics.
[1] S. Kitahama et al., J. Stat. Mech. 013101 (2024).
[2] H. Hodaei et al., Nature 23280 (2017).