PTsymmetry in the non-Hermitian Su-Schrieffer-Heeger model with complex boundary potentials

Abstract

We study the parity-and time-reversal (PT ) symmetric non-Hermitian Su-Schrieffer-Heeger (SSH) model with two conjugated imaginary potentials ±iγ at two end sites. The SSH model is known as one of the simplest two-band topological models which has topologically trivial and nontrivial phases. We find that the non-Hermitian terms can lead to different effects on the properties of the eigenvalues spectrum in topologically trivial and nontrivial phases. In the topologically trivial phase, the system undergos an abrupt transition from unbroken PT -symmetry region to spontaneously broken PT -symmetry region at a certain γc, and a second transition occurs at another transition point γ c ′ when further increasing the strength of the imaginary potential γ. But in the topologically nontrivial phase, the zero-mode edge states become unstable for arbitrary nonzero γ and the PT -symmetry of the system is spontaneously broken, which is characterized by the emergence of a pair of conjugated imaginary modes.

Quasi-Hermitian Lattices with Imaginary Zero-Range Interactions

“…Regarding model-building schemes for finite quasi-hermitian Hamiltonians, different techniques may be employed to yield different useful results. The correspondence between useful models of solid state physics and lattice quasi-hermitian operators has proven fruitful very recently [15,16]. Also, the correspondence between (non-normalized) orthogonal polynomials [34] and quantum-mechanical matrix models in has produces some interesting output [35,36].…”

“…5, which surpasses the previously examined toy models (e.g. [15]) both in sparsity and simplicity of the resulting pseudometric matrix elements.…”

“…Finite-dimensional toy models, in addition to having diverse applications in quantum and solid-state physics per se [13,14,15,16], provide also vast possibilities for the description of various physical phenomena in simplified scenarios. Indeed, finite quasi-hermitian Hamiltonians have been succesfully used to model quantum phase transitions [17], quantum catastrophes [18] or even simplified big-bang scenarios [19].…”

Topological phase in a non-Hermitian PT symmetric system

“…Does there exist a topologically nontrivial system described by non-Hermitian Hamiltonian? This problem was considered by some authors [16,17,18,19,20,21]. Hu and Hughes [16] and Esaki et al [17] studied non-Hermitian generalization of topologically insulating phase at almost the same time.…”

“…Schomerus considered a one dimensional nonHermitian tight binding lattice with staggered tunneling amplitude and showed that the system admits complex spectrum [19]. Another attempt has recently been made to find non-Hermitian Hamiltonian admitting topological insulator phase [20]. Zhu, Lu and Chen specifically considered non-Hermitian Su-Schrieffer-Heeger model with two conjugated imaginary potential located at the edges of the system [20].…”