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arXiv:2610.27436

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

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

cond-mat.mes-hallcond-mat.dis-nnquant-phSubmitted Oct 20, 2026• Announced Oct 21, 2026
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Abstract

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.

Comments
7 figures, 13 pages

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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 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.
A dimerized fermion chain, described by Su-Schrieffer-Heeger (SSH) model, is a well-known example of a one-dimensional system with a nontrivial band topology. An interplay of disorder and topological ordering in the SSH model is of great interest owing to experimental advancements in synthesized quantum simulators. In this paper, we investigate a special sort of a disorder when intercell hopping amplitudes are random. Using a definition for Z2{\mathbb{Z}}_{2}Z2​-topological invariant $\ensuremath{\nu}\ensuremath{\in}{0;1}$ in terms of a non-Hermitian part of the total Hamiltonian, we calculate $\ensuremath{\langle}\ensuremath{\nu}\ensuremath{\rangle}$ averaged by random realizations. This allows to find: (i) an analytical form of the critical surface that separates phases of distinct topological orders and (ii) finite-size fluctuations of $\ensuremath{\nu}$ for arbitrary disorder strength. Numerical simulations of the edge modes formation and gap suppression at the transition are provided for the finite-size system. In the end, we discuss a band-touching condition derived within the averaged Green's function method for a thermodynamic limit.
We investigate the non-Hermitian skin effect (NHSE) and topological phases in a ladder model with staggered nonreciprocal inter-leg hopping, consisting of an Su-Schrieffer-Heeger (SSH) chain coupled to a normal tight-binding chain. By tuning the system parameters, we show that the direction of the NHSE under open boundary conditions can be reversed and can even become energy dependent. The NHSE is further characterized by the spectral winding number under periodic boundary conditions. We further demonstrate that the inter-leg coupling significantly enlarges the topologically nontrivial parameter regime. Remarkably, the zero-energy topological edge modes reside on different legs of the ladder and are characterized by real-space winding numbers W=±1W=\pm1W=±1. Furthermore, increasing the nonreciprocity of the inter-leg hopping modifies the topological phase boundaries and eventually drives the system into a topologically trivial phase. Our results establish staggered nonreciprocal inter-leg hopping as an effective mechanism for engineering both the non-Hermitian skin effect and topological phases in ladder systems.
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.
We investigate quantum correlations and entanglement in a non-Hermitian quantum system modeled by a 2D stacked Su–Schrieffer–Heeger (SSH) lattice incorporating nonreciprocal hopping amplitudes and balanced on-site gain and loss. Focusing on the interplay between non-Hermiticity, topology, and open-boundary conditions, we analyze how these factors shape bipartite entanglement properties, characterized through the entanglement spectrum and entanglement negativity ( E N ). By examining the complex energy spectrum under open boundary conditions, we identify critical points associated with the closing of complex energy gaps, which significantly influence entanglement structure and signal topological phase transitions. Our findings reveal that boundary-localized non-Bloch modes and nonreciprocal couplings can induce highly tunable and unconventional entanglement features, absent under periodic boundary conditions. These results highlight the breakdown of conventional bulk-boundary correspondence and underscore the utility of entanglement measures in diagnosing non-Hermitian topological phases. Beyond advancing the fundamental understanding of quantum correlations in open systems, our study suggests potential pathways to engineer quantum devices and topological materials where gain, loss, and nonreciprocity are intrinsic elements.
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.