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/

[1] Kitaev A.Yu., “Unpaired Majorana fermions in quantum wires”, Physics-Uspekhi, 44:10 suppl. (2001), s131–s136 | DOI

[2] von Oppen F., Peng Yang, Pientka F., “Topological superconducting phases in one dimension”, Topological Aspects of Condensed Matter Physics, Oxford University Press, 2017, 387–450 | DOI | MR

[3] Hasan M.Z., Kane C.L., “Colloquium: Topological insulators”, Reviews of Modern Physics, 82:4 (2010), 3045–3067 | DOI

[4] Asbóth J.K., Oroszlány L., Pályi A., A short course on topological insulators. Band structure and edge states in one and two dimensions, Springer, Cham, 2016 | DOI | MR | Zbl

[5] Okuma Nobuyuki, Sato Masatoshi, “Non-Hermitian topological phenomena: a review”, Annual Review of Condensed Matter Physics, 14 (2023), 83–107 | DOI

[6] Yao Shunyu, Wang Zhong, “Edge states and topological invariants of non-Hermitian systems”, Physical Review Letters, 121:8 (2018), 086803 | DOI

[7] Ashida Yuto, Gong Zongping, Ueda Masahito, “Non-Hermitian physics”, Advances in Physics, 69:3 (2020), 249–435 | DOI

[8] Gong Zongping, Ashida Yuto, Kawabata Kohei, Takasan Kazuaki, Higashikawa Sho, Ueda Masahito, “Topological phases of non-Hermitian systems”, Physical Review X, 8:3 (2018), 031079 | DOI

[9] Bergholtz E.J., Budich J.C., Kunst F.K., “Exceptional topology of non-Hermitian systems”, Reviews of Modern Physics, 93:1 (2021), 015005 | DOI | MR

[10] Lin Rijia, Tai Tommy, Li Linhu, Lee Ching Hua, “Topological non-Hermitian skin effect”, Frontiers of Physics, 18:5 (2023), 53605 | DOI

[11] Banerjee Ayan, Sarkar Ronika, Dey Soumi, Narayan Awadhesh, “Non-Hermitian topological phases: principles and prospects”, Journal of Physics: Condensed Matter, 35:33 (2023), 333001 | DOI

[12] Su W.P., Schrieffer J.R., Heerger A.J., “Solitons in polyacetilene”, Physical Review Letters, 42:25 (1979), 1698–1701 | DOI

[13] Bender C.M., Boettcher S., “Real spectra in non-Hermitian Hamiltonians having PT simmetry”, Physical Review Letters, 80:24 (1998), 5243–5246 | DOI | MR | Zbl

[14] Lieu S., “Topological phases in the non-Hermitian Su–Schrieffer–Heeger model”, Physical Review B, 97:4 (2018), 045106 | DOI | MR

[15] Chuburin Yu.P., Tinyukova T.S., “The emergence of bound states in a superconducting gap at the topological insulator edge”, Physics Letters A, 384:27 (2020), 126694 | DOI | MR

[16] Tinyukova T.S., Chuburin Yu.P., “Majorana states near an impurity in the Kitaev infinite and semi-infinite model”, Theoretical and Mathematical Physics, 200:1 (2019), 1043–1052 | DOI | DOI | MR | Zbl

[17] Taylor J.R., Scattering theory. The quantum theory of nonrelativistic collisions, Courier Corporation, New York, 2006

[18] Edwards R.E., Functional analysis: theory and applications, Courier Corporation, New York, 1995 | MR