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arXiv:2610.29316

Boundary exceptional point driven chiral switch of topological edge states

Bikashkali Midya, Barsa Rani Sahu

quant-phcond-mat.otherSubmitted Oct 21, 2026• Announced Oct 22, 2026
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Abstract

We theoretically investigate the interplay of topology and localized non-Hermiticity in a finite Su-Schrieffer-Heeger chain characterized by non-Hermitian potentials at its boundaries. By tuning the boundary gain and loss parameters, we exploit the finite-size hybridization of two mid-gap topological edge states to analytically derive the exact coordinates of boundary-induced exceptional points (EPs), $Γ_{\rm EP}=\pm i v^{N}/w^{N-1}$, at which these states undergo coalescence. We demonstrate that dynamically encircling these boundary EPs facilitates a robust, chiral edge state-transfer protocol. Depending on the orientation of the encircling loop, this protocol allows a topological edge state localized at one boundary to be either transferred to the opposite edge with perfect fidelity or returned to its starting position through a double switching process. Importantly, since the non-Hermiticity remains strictly confined to the boundaries, this chiral transport occurs without affecting the energy spectrum of the bulk bands. These results establish a minimal framework for a large-scale topological chiral switch that is experimentally verifiable and capable of being controlled through boundary non-Hermitian driving.

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We theoretically investigate the interplay of topology and localized non-Hermiticity in a finite Su-Schrieffer-Heeger chain characterized by non-Hermitian potentials at its boundaries. By tuning the boundary gain and loss parameters, we exploit the finite-size hybridization of two mid-gap topological edge states to analytically derive the exact coordinates of boundary-induced exceptional points (EPs), ΓEP=±ivN/wN−1Γ_{\rm EP}=\pm i v^{N}/w^{N-1}ΓEP​=±ivN/wN−1, at which these states undergo coalescence. We demonstrate that dynamically encircling these boundary EPs facilitates a robust, chiral edge state-transfer protocol. Depending on the orientation of the encircling loop, this protocol allows a topological edge state localized at one boundary to be either transferred to the opposite edge with perfect fidelity or returned to its starting position through a double switching process. Importantly, since the non-Hermiticity remains strictly confined to the boundaries, this chiral transport occurs without affecting the energy spectrum of the bulk bands. These results establish a minimal framework for a large-scale topological chiral switch that is experimentally verifiable and capable of being controlled through boundary non-Hermitian driving.
Non-Hermitian systems exhibit a variety of unique features rooted in the presence of exceptional points (EPs). The distinct topological structure in the proximity of an EP gives rise to counterintuitive behaviors absent in Hermitian systems, which emerge after encircling the EP either quasistatically or dynamically. However, experimental exploration of EP encirclement in quantum systems, particularly those involving high-order EPs, remains challenging due to the difficulty of coherently controlling more degrees of freedom. In this work, we experimentally investigate the eigenvalue braiding and state transfer arising from the encirclement of EP in a three-dimensional non-Hermitian quantum system using superconducting circuits. We characterize the second- and third-order EPs through the coalescence of eigenvalues. Then we reveal the topological structure near the EP3 by quasistatically encircling it along various paths with three independent parameters, which yields the eigenvalue braiding described by the braid group B 3 . Additionally, we observe chiral state transfer between three eigenstates under a fast driving scheme when no EPs are enclosed, while time-symmetric behavior occurs when at least one EP is encircled. Our findings offer insights into understanding non-Hermitian topological structures and the manipulation of quantum states through dynamic operations.
Topological transitions in non-Hermitian systems are generally boundary sensitive: a point-gap winding transition under periodic boundary condition (PBC) and a non-Bloch bulk real-line-gap transition under open boundary condition (OBC) at Re(E)=0\mathrm{Re}(E)=0Re(E)=0 are governed by different spectra and therefore need not coincide. Here we show, for a class of chiral non-Hermitian Su--Schrieffer--Heeger (SSH)-type lattices, that these two criticalities can be locked by an exceptional-point-constrained (EP-constrained) parameter evolution. The key requirement is not the occurrence of isolated exceptional points, but the persistence of a zero-energy Bloch degeneracy along the entire sweep, which is generically exceptional in the non-Hermitian regime. In an analytically tractable limit of an extended non-Hermitian SSH chain, the EP-constrained manifolds and both transition boundaries are obtained in closed form, making the locking explicit. Away from this limit, numerical generalized-Brillouin-zone (GBZ) calculations confirm the correspondence for representative constrained sweeps, whereas unconstrained paths show that isolated exceptional points or Hermitian degeneracies do not enforce locking. We further verify the mechanism in a spinful four-band extension with branch-resolved GBZs, including strongly branch-imbalanced regimes. These results establish a path-dependent diagnostic principle: along EP-constrained sweeps in this SSH-type class, changes in PBC point-gap winding can indicate OBC non-Bloch bulk real-line-gap transitions and the corresponding changes in zero-energy boundary modes.
Topologically ordered phases have robust degenerate ground states against the local perturbations, providing a promising platform for fault-tolerant quantum computation. Despite of the non-local feature of the topological order, we find that local non-Hermitian perturbations can induce the transition between the topologically ordered ground states. In this work, we study the toric code in the presence of non-Hermitian perturbations. By controlling the non-Hermiticity, we show that non-orthogonal ground states can exhibit an eigenstate coalescence and have the spectral singularity, known as an exceptional point (EP). We explore the potential of the EPs in the control of topological order. Adiabatic encircling EPs allows for the controlled switching of eigenstates, enabling dynamic manipulation between the ground state degeneracy. Interestingly, we show a property of our scheme that arbitrary strengths of local perturbations can induce the EP and eigenstate switching. Finally, we also show the orientation-dependent behavior of non-adiabatic transitions (NAT) during the dynamic encirclement around an EP. Our work shows that control of the non-Hermiticity can serve as a promising strategy for fault-tolerant quantum information processing.
We investigate a non-Hermitian quantum battery based on the Su-Schrieffer-Heeger (SSH) lattice, charged through a parity-time (PT)-symmetric protocol that alternates gain and loss between the two sublattices. The interplay between lattice topology and non-Hermiticity gives rise to both bulk and edge exceptional points (EPs), which govern the charging dynamics. In the topological regime, an edge-state EP appears at a smaller gain-loss strength than the bulk thresholds and gives rise to an additional edge-broken regime absent in the trivial configuration. This topology-specific spectral structure is reflected in the charging dynamics, where the topological phase exhibits more favorable transient and long-time performance in the representative non-Hermitian regimes considered here. We further examine the corresponding Lindblad dynamics, identifying the non-Hermitian model as the conditional no-jump description of the same gain-loss processes. The Lindblad results show that the topological advantage remains visible at the level of stored energy, extractable work, and extractable fraction under unconditional open-system evolution. These findings demonstrate that topology constitutes a genuine physical resource for enhancing the performance of quantum batteries.
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.
The zero-mode corner states in the gap of two-dimensional non-Hermitian Su-Schrieffer-Heeger model are robust to infinitesimal perturbations that preserve chiral symmetry. However, we demonstrate that this general belief is no longer valid in large-sized systems. To reveal the higher-order topology of non-Hermitian systems, we establish a correspondence between the stable zero-mode singular states and the topologically protected corner states of energy spectrum in the thermodynamic limit. Within this framework, the number of zero-mode singular values is directly linked to the number of mid-gap corner states. The winding numbers in real space can be defined to count the number of stable zero-mode singular states. Our results formulate a bulk-boundary correspondence for both static and Floquet non-Hermitian systems, where topology arises intrinsically from the non-Hermiticity, even without symmetries.