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arXiv:2601.20479

Multiple mobility rings in non-Hermitian Su-Schrieffer-Heeger chain with quasiperiodic potentials

Guan-Qiang Li, Zhi-Yu Lin, You-Jiao Dong, Ya-Feng Xue, Chun-Yang Ren, Ping Peng

quant-phSubmitted Jan 28, 2026• Announced Jan 29, 2026
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Abstract

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.

Related papers

Competing skin effect and quasiperiodic localization in the non-Hermitian Su-Schrieffer-Heeger chain: Reentrant delocalization, spectral topology destruction, and entanglement suppression

Souvik Ghosh

We investigate the interplay between the non-Hermitian skin effect and Aubry-André-Harper (AAH) quasiperiodic disorder in a one-dimensional Su-Schrieffer-Heeger (SSH) chain with nonreciprocal hopping. By exact diagonalization, transfer-matrix analysis, and an analytical similarity-transformation argument, we map the full ( , $δ$) phase diagram, where A is the AAH modulation strength and the nonreciprocity parameter. We identify five distinct regimes: ( ) topological with extended bulk, (II) AAH-localized, (III) skin-localized, (IV) fully localized, and a previously unreported (V) competition regime exhibiting reentrant partial delocalization, in which intermediate quasiperiodic disorder disrupts the directional skin accumulation before ultimately Anderson-localizing all states. Using phase-averaged diagnostics and finite-size scaling, we confirm that the reentrant regime is robust, characterized by a non-monotonic inverse participation ratio that sharpens with increasing system size. We derive an analytical expression for the modified localization boundary $λ_{c}(δ)=2\sqrt{v_{eff}w}$ with $v_{vff}=\sqrt{v^{2}-δ^{2}}$, which agrees with numerical Lyapunov exponent calculations. We further show that quasiperiodic disorder progressively unwinds the complex spectral loops, destroying the point-gap topology at a critical strength distinct from the band-topological transition ; that the skin effect suppresses entanglement entropy to near-zero values while sufficiently strong AAH disorder partially restores it ; and that the SSH sublattice structure absent in the widely studied non-Hermitian AAH chain is essential for producing the five-phase landscape, as demonstrated by direct comparison with the non-dimerized limit.

cond-mat.mes-hallCross-listedarXiv:2603.20330•Mar 23, 2026

Interaction and non-Hermiticity controlled transmission in extended Su-Schrieffer-Heeger models

Syeda Rafisa Rahaman, Shreekantha Sil, Nilanjan Bondyopadhaya

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.

cond-mat.mes-hallCross-listedarXiv:2606.15245•Jun 16, 2026

Transitions and Critical Divergences in Periodically Hopping Modulated Su-Schrieffer-Heeger Chains

Surajit Mandal, Satyaki Kar

We use a curvature renormalization group (CRG) approach to study the topological phase transitions in a Su-Schrieffer-Heeger chain and its extensions coming from periodic hopping modulations. A curvature function is defined in terms of system parameters near high-symmetry points where the divergence of this function at critical points, in analogy to usual phase transitions, signals a topological phase transition. According to this theory, the phase transition line for the two-site Su-Schrieffer-Heeger (SSH) model is visible at the critical line Δ= 0 where the curvature function diverges. Our study involves this model and also the modulated one with periodicity of four lattice spacing where the curvature function not only diverges at the topological phase transition point (Dirac-like) |Δ/t| = \sqrt(2) but also shows faster divergence at the non-topological gapless point Δ= 0. We further notice faster divergence of correlation length for Δ-> 0 as compared to that for the |Δ/t| -> \sqrt(2) resulting in two different sets of critical exponents making them lie in different universality classes. The edge state exhibits very slow decay into the bulk near the Δ= 0 point while a much quicker decay from edge into bulk is discernible around the |Δ/t| = \sqrt(2) point. We also continue similar analysis for a SSH model with hopping periodicity of eight lattice spacing.

arXiv:2608.18706•Aug 19, 2026•0 citations

Zero-energy states and non-Hermitian skin effect in the infinite double-barrier and finite Su–Schrieffer–Heeger models

Tat'yana Sergeevna Tinyukova, Yu. P. Chuburin

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.

Theoretical and Mathematical Physics•May 1, 2026•0 citations

Steering of topological criticality in the Su-Schrieffer-Heeger chain via non-Hermitian substitutional impurities

Juan A. Cañas, Guo-Qing Zhang, A. Martín-Ruiz

We investigate the topological phase in a one-dimensional Su-Schrieffer-Heeger (SSH) chain in the presence of a finite concentration of non-Hermitian substitutional impurities. Our primary focus is the discovery of a deterministic mechanism to actively reconfigure the topological phase boundaries by introducing site-dependent, non-reciprocal intracell and intercell hopping amplitudes. Specifically, breaking the internal structural symmetry of the non-reciprocal impurity hoppings induces a targeted macroscopic displacement of the critical point. This mechanism allows for the controlled expansion or compression of the topological phase strictly via local defect asymmetry. We validate this boundary displacement through finite-size scaling analysis. The extracted correlation length critical exponents ($ν\approx 1.455$ and $ν\approx 1.397$ for symmetric and asymmetric configurations, respectively) confirm a disorder-induced departure from the pristine SSH universality class, with the exponent diverging at high defect densities. We also report an impurity-induced real-to-complex spectral transition geometrically characterized by the Non-Hermitian Skin Effect. Ultimately, our results establish how isolated non-Hermitian asymmetries cooperatively interact to deterministically shift macroscopic topological protection.

cond-mat.mes-hallCross-listedarXiv:2610.27436•Oct 21, 2026

Mapping the topology-localization phase diagram with quasiperiodic disorder using a programmable superconducting simulator

Xuegang Li, Huikai Xu, Junhua Wang +23 more

We explore a topology-localization phase diagram by simulating a one-dimensional Su-Schrieffer-Heeger model with quasiperiodic disorder using a programmable superconducting simulator. We experimentally map out and identify various trivial and topological phases with extended, critical, and localized bulk states. We find that with increasing disorder strength, some extended states can be first replaced by localized states and then by critical states before the system finally becomes fully localized. The critical states exhibit typical features such as multifractality and self-similarity, which lead to surprisingly rich phases with different types of mobility edges and scaling behaviors on the phase boundaries. Our results shed light on the investigation of the topological and localization phenomena in condensed-matter physics. Published by the American Physical Society 2024

arXiv:2301.12138•Physical Review Research•Nov 5, 2024•21 citations
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.
We investigate the interplay between the non-Hermitian skin effect and Aubry-André-Harper (AAH) quasiperiodic disorder in a one-dimensional Su-Schrieffer-Heeger (SSH) chain with nonreciprocal hopping. By exact diagonalization, transfer-matrix analysis, and an analytical similarity-transformation argument, we map the full ( , δδδ) phase diagram, where A is the AAH modulation strength and the nonreciprocity parameter. We identify five distinct regimes: ( ) topological with extended bulk, (II) AAH-localized, (III) skin-localized, (IV) fully localized, and a previously unreported (V) competition regime exhibiting reentrant partial delocalization, in which intermediate quasiperiodic disorder disrupts the directional skin accumulation before ultimately Anderson-localizing all states. Using phase-averaged diagnostics and finite-size scaling, we confirm that the reentrant regime is robust, characterized by a non-monotonic inverse participation ratio that sharpens with increasing system size. We derive an analytical expression for the modified localization boundary λc(δ)=2veffwλ_{c}(δ)=2\sqrt{v_{eff}w}λc​(δ)=2veff​w​ with vvff=v2−δ2v_{vff}=\sqrt{v^{2}-δ^{2}}vvff​=v2−δ2​, which agrees with numerical Lyapunov exponent calculations. We further show that quasiperiodic disorder progressively unwinds the complex spectral loops, destroying the point-gap topology at a critical strength distinct from the band-topological transition ; that the skin effect suppresses entanglement entropy to near-zero values while sufficiently strong AAH disorder partially restores it ; and that the SSH sublattice structure absent in the widely studied non-Hermitian AAH chain is essential for producing the five-phase landscape, as demonstrated by direct comparison with the non-dimerized limit.
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 use a curvature renormalization group (CRG) approach to study the topological phase transitions in a Su-Schrieffer-Heeger chain and its extensions coming from periodic hopping modulations. A curvature function is defined in terms of system parameters near high-symmetry points where the divergence of this function at critical points, in analogy to usual phase transitions, signals a topological phase transition. According to this theory, the phase transition line for the two-site Su-Schrieffer-Heeger (SSH) model is visible at the critical line Δ= 0 where the curvature function diverges. Our study involves this model and also the modulated one with periodicity of four lattice spacing where the curvature function not only diverges at the topological phase transition point (Dirac-like) |Δ/t| = \sqrt(2) but also shows faster divergence at the non-topological gapless point Δ= 0. We further notice faster divergence of correlation length for Δ-> 0 as compared to that for the |Δ/t| -> \sqrt(2) resulting in two different sets of critical exponents making them lie in different universality classes. The edge state exhibits very slow decay into the bulk near the Δ= 0 point while a much quicker decay from edge into bulk is discernible around the |Δ/t| = \sqrt(2) point. We also continue similar analysis for a SSH model with hopping periodicity of eight lattice spacing.
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.
We investigate the topological phase in a one-dimensional Su-Schrieffer-Heeger (SSH) chain in the presence of a finite concentration of non-Hermitian substitutional impurities. Our primary focus is the discovery of a deterministic mechanism to actively reconfigure the topological phase boundaries by introducing site-dependent, non-reciprocal intracell and intercell hopping amplitudes. Specifically, breaking the internal structural symmetry of the non-reciprocal impurity hoppings induces a targeted macroscopic displacement of the critical point. This mechanism allows for the controlled expansion or compression of the topological phase strictly via local defect asymmetry. We validate this boundary displacement through finite-size scaling analysis. The extracted correlation length critical exponents (ν≈1.455ν\approx 1.455ν≈1.455 and ν≈1.397ν\approx 1.397ν≈1.397 for symmetric and asymmetric configurations, respectively) confirm a disorder-induced departure from the pristine SSH universality class, with the exponent diverging at high defect densities. We also report an impurity-induced real-to-complex spectral transition geometrically characterized by the Non-Hermitian Skin Effect. Ultimately, our results establish how isolated non-Hermitian asymmetries cooperatively interact to deterministically shift macroscopic topological protection.
We explore a topology-localization phase diagram by simulating a one-dimensional Su-Schrieffer-Heeger model with quasiperiodic disorder using a programmable superconducting simulator. We experimentally map out and identify various trivial and topological phases with extended, critical, and localized bulk states. We find that with increasing disorder strength, some extended states can be first replaced by localized states and then by critical states before the system finally becomes fully localized. The critical states exhibit typical features such as multifractality and self-similarity, which lead to surprisingly rich phases with different types of mobility edges and scaling behaviors on the phase boundaries. Our results shed light on the investigation of the topological and localization phenomena in condensed-matter physics. Published by the American Physical Society 2024