Ken Mochizuki

Department of Applied Physics
Hokkaido University
Japan

Naomichi Hatano

Institute of Industrial Science
The University of Tokyo
Japan

Joshua Feinberg

Department of Mathematics
University of Haifa
Israel

Hideaki Obuse

Department of Applied Physics
Hokkaido University
Japan

Statistical properties of eigenvalues in a non-Hermitian SSH model with random hopping terms

We explore statistical properties of eigenvalues in Su-Schrieffer-Heeger model with imaginary on site potentials (non-Hermitian SSH model), whose hopping terms are randomly distributed spatially. It is proved that, originating from a structure of the Hamiltonian, eigenvalues can be entirely real without PT symmetry (Parity and Time-reversal symmetry) in a certain parameter region. Also, we clarify that level statistics obey that of Gaussian orthogonal ensemble (GOE) when the Hamiltonian has entirely real spectra, showing a general fact that a non-Hermitian Hamiltonian whose eigenvalues are real is mapped to a Hermitian Hamiltonian which shares the same symmetries with the original Hamiltonian. When imaginary eigenvalues exist, it is shown that the density of states (DOS) becomes zero at the origin and diverges along the imaginary axis. The divergence of DOS originates from Dyson singularity in chiral symmetric 1D Hermitian systems, while the analytically derived asymptote of DOS is different from that in such systems.