We study the transport characteristics of an extended version of the Su-Schrieffer-Heeger (SSH) model with next-nearest-neighbor (NNN) interactions and non-Hermitian onsite energies. We observed that transport in such a system is significantly modified by the NNN interaction and the non-Hermitian terms. The transmission coefficient exhibits oscillatory behavior as the strength of the NNN interaction varies in a fixed-length chain. Moreover, the transmission coefficient also shows oscillation with system size for a fixed strength of the NNN interaction. We find that novel oscillatory behavior of the transmission coefficient, arising form the NNN interaction, is a unique feature of such a model and has not been reported previously. The presence of the non-Hermitian terms also enhances/reduces the transmission coefficient depending on the values of the other system parameters like intra-, inter- and NNN hopping. It appears from our study that both the NNN interaction and the non-Hermiticity introduce significant changes in the transport properties of the extended SSH chain, which are not observed in the standard Hermitian nearest-neighbour variant of the SSH model.
We investigate phase transitions in the extended Su-Schrieffer-Heeger (SSH) model with next-nearest-neighbor hoppings and an imaginary staggered chemical potential. In the presence of small non-Hermiticity, exceptional points emerge in pairs from the gap-closing momenta near the topological phase boundaries of the Hermitian limit. Utilizing the Krylov spread complexity and entanglement entropy, we analyze two dynamical protocols: (i) preparing the non-Hermitian ground state via a unitary transformation, and (ii) evolving the system under the non-Hermitian Hamiltonian. We show that the spread complexity, and long-time spread complexity as well as entanglement entropy can effectively signal phase transitions in the first and second protocols, respectively. To unravel the detailed structure of the transitions, we introduce the momentum-resolved complexity that identifies the characteristic modes and tracks their evolution with the driving parameter. In the regime where the system possesses a purely imaginary spectrum, we further identify dynamical phases based on the saturation behavior of the spread complexity. The entanglement entropy is also found to exhibit similar saturation behavior, thereby providing a more experimentally accessible probe of the dynamical phases.
The localization property of a non-Hermitian Su-Schrieffer-Heeger (SSH) chain with quasi-periodic on-site potential is investigated. In contrast to the preceding investigations, the quantum phase transition between localized state and extended one is achieved by adjusting the strength of intracellular or intercellular hopping. The energy spectra and eigenstate distributions of the system's Hamiltonian near the boundary of the phase transition exhibit different behaviors when the Hermiticity, non-Hermiticity and mosaic modulation of the quasi-periodic potential are considered, respectively. The existence of the mobility ring is revealed in the non-Hermitian SSH chain by studying of the critical behaviors near the boundary. More interestingly, the multiple mobility rings emerge when the period number of the mosaic modulation is increased. The result is helpful for the investigation of the localization-delocalization transition in the SSH-type system under the combined action of the non-Hermiticity and quasi-periodicity.
Abstract We analytically study zero-energy eigenstates for two non-Hermitian models based on the Su–Schrieffer–Heeger (SSH) chain. The first model is an infinite non-Hermitian SSH chain with nonreciprocal hoppings to a neighboring site and two barriers. We find analytical expressions for the eigenfunctions, including those that describe resonant states. For resonant states, an analogue of the non-Hermitian skin effect is observed. For the second model, a finite non-Hermitian SSH chain with nonreciprocal hoppings with an even or odd number of sites, we also find the eigenfunctions and observe the non-Hermitian skin effect. All results are obtained using the derived Green’s function of the infinite non-Hermitian SSH chain.
Non-reciprocal lattices offer a flexible setting for directional wave transport, raising the question of how enhanced internal scattering translates into transmission between fixed external ports. We address this question for non-reciprocal Su--Schrieffer--Heeger (SSH) chains with staggered gain and loss by relating the reference-dependent insertion kernel
Kp=VGpV to the coherent transmission intensity
T. On a fixed finite graph, a strong-insertion expansion gives a contribution proportional to
γ1−d, whose coefficient is the signed sum of shortest directed paths of length
d. When this sum is nonzero, it sets the leading behavior independently of fixed diagonal losses; when it cancels, those losses can enter the first surviving higher-order term. For a fixed cross-sublattice endpoint channel, transmission has a strictly negative slope at every nonzero differentiable stationary point of the kernel magnitude. In the weak-insertion regime, the reference-system coefficient
χ=−ReTr[(G0pZ)2] predicts the initial transmission change for symmetric SSH ports, and
χ>0 together with a strictly stable baseline guarantees local stable enhancement. Finite-chain calculations and driven dynamics connect these results to observable response and distinguish asymptotic convergence from transient settling. A strictly dissipative short-chain example exhibits local enhancement without net power gain. Together, these results separate graph-path structure, coherent port response, and dynamical establishment, providing channel-specific criteria for interpreting internal scattering.
| > 1 are observed in this study of a periodically driven extended Su-Schrieffer-Heeger (E-SSH) model with a cyclic parameter. Besides the standard intra-dimer and the nearest-neighbor inter-dimer hopping of the SSH model, an additional next-nearest-neighbor hopping is considered in the E-SSH model. The cyclic parameter, which plays the role of a synthetic dimension, is invoked as a modulation of the hopping strengths. A rigorous analysis of different phase diagrams has shown multiple Floquet topological phase transitions among the high Chern number phases. These phase transitions can be controlled by the strength and frequency of the periodic driving. Instead of applying perturbation theory, the whole analysis is done by Floquet replica technique. This gives a freedom to study high as well as low-frequency effects on the system by considering less or more number of photon sectors. This system can be experimentally realized through a pulse sequence scheme in the optical lattice setup.
We investigate the interacting non-Hermitian Su-Schrieffer-Heeger (SSH) model, focusing on the interplay between topology and charge ordering. Using a real-space topological marker, charge correlations, and the complex many-body spectrum, we map out the phase diagram under periodic and open boundary conditions. We show that the topological marker remains a robust diagnostic of non-Hermitian topological phases in the presence of interactions and consistently signals their breakdown at the onset of a charge density wave (CDW). We further demonstrate that non-Hermiticity enhances interaction effects: While moderate changes occur under periodic boundary conditions, open boundary conditions lead to a pronounced amplification of staggered charge correlations near exceptional points. This enhancement arises from the accumulation of low-energy states near exceptional points, which promotes electronic instabilities and strengthens CDW tendencies.