Geodesic
Eigenvalues and eigenfunctions of the perturbed non-Hermitian SSH Hamiltonian with PT symmetry
Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 62 (2023), pp. 87-95

Voir la notice de l'article provenant de la source Math-Net.Ru

In the paper we find near-zero eigenvalues (their physical meaning is the electron energy) and eigenfunctions describing the electronic states of the non-Hermitian SSH Hamiltonian for an infinite chain with PT symmetry, perturbed by a $\delta$-shaped potential. We prove that for a small non-Hermitian parameter there are two (generalized) eigenvalues of multiplicity one, and, in contrast to the Hermitian model, the corresponding (generalized) eigenfunctions depending on the parameters of the system can either increase exponentially (which corresponds to resonant, i.e., decaying states) or decrease exponentially (which corresponds to bound states) as $|n|\to\infty$.
Keywords: eigenvalue, eigenfunction, non-Hermitian SSH Hamiltonian, PT symmetry, Green’s function. 
@article{IIMI_2023_62_a6,
     author = {T. S. Tinyukova and Yu. P. Chuburin},
     title = {Eigenvalues and eigenfunctions of the perturbed {non-Hermitian} {SSH} {Hamiltonian} with {PT} symmetry},
     journal = {Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta},
     pages = {87--95},
     publisher = {mathdoc},
     volume = {62},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IIMI_2023_62_a6/}
}
TY  - JOUR
AU  - T. S. Tinyukova
AU  - Yu. P. Chuburin
TI  - Eigenvalues and eigenfunctions of the perturbed non-Hermitian SSH Hamiltonian with PT symmetry
JO  - Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta
PY  - 2023
SP  - 87
EP  - 95
VL  - 62
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IIMI_2023_62_a6/
LA  - ru
ID  - IIMI_2023_62_a6
ER  - 
%0 Journal Article
%A T. S. Tinyukova
%A Yu. P. Chuburin
%T Eigenvalues and eigenfunctions of the perturbed non-Hermitian SSH Hamiltonian with PT symmetry
%J Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta
%D 2023
%P 87-95
%V 62
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IIMI_2023_62_a6/
%G ru
%F IIMI_2023_62_a6
T. S. Tinyukova; Yu. P. Chuburin. Eigenvalues and eigenfunctions of the perturbed non-Hermitian SSH Hamiltonian with PT symmetry. Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 62 (2023), pp. 87-95. http://geodesic.mathdoc.fr/item/IIMI_2023_62_a6/