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Solvable semi-infinite Fock-state-lattice Su-Schrieffer-Heeger model: Stable topological zero modes and the non-Hermitian bound effect

Xing Yao Mi1,2, Yong-Chun Liu3, Zhi Jiao Deng1,2,4,*, Chun Wang Wu1,2,†, and Ping Xing Chen1,2,5

  • 1Institute for Quantum Science and Technology, College of Science, National University of Defense Technology, Changsha, Hunan 410073, China
  • 2Hunan Key Laboratory of Mechanism and Technology of Quantum Information, Changsha, Hunan 410073, China
  • 3State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics, Frontier Science Center for Quantum Information, Tsinghua University, Beijing 100084, China
  • 4Key Laboratory of Low Dimensional Quantum Structures and Quantum Control of Ministry of Education, Hunan Normal University, Changsha, Hunan 410081, China
  • 5Hefei National Laboratory, Hefei, Anhui 230088, China

  • *Contact author: dengzhijiao926@hotmail.com
  • †Contact author: cwwu@nudt.edu.cn
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Phys. Rev. Research 7, 043151 – Published 10 November, 2025

DOI: https://doi.org/10.1103/dklw-2bfv

Abstract

Fock-state lattice (FSL) offers a powerful quantum simulator for topological phenomena due to the unbounded scalability and ease of implementation. Nevertheless, the unique topological properties induced by its site-dependent coupling have remained elusive, mainly due to the challenge of handling an infinite state space without translational symmetry. Here, we rigorously analyze the topological features of a semi-infinite FSL-based Su-Schrieffer-Heeger (SSH) model, in both Hermitian and non-Hermitian realms, by mapping it to the solvable Jaynes-Cummings model via a unitary displacement transformation. We find a topological zero mode persisting across all parameter regimes, which is more stable than the conventional SSH model. It originates from the bound state at the inherent domain wall under anisotropic conditions. With gain and loss introduced, we predict a non-Hermitian bound effect, i.e., any state overlapping with the bound state will quickly stabilize to the domain wall, with the minimal stabilization time occurring in the vicinity of exceptional point. The parity-time phase transition can be observed by the oscillating-to-steady crossover of dynamics in the subspace orthogonal to the bound state. Furthermore, a concrete experimental proposal based on the trapped-ion setup is provided.

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Phys. Rev. Research 7, 043151– Published 10 November, 2025
  • Received 21 June 2025
  • Accepted 9 October 2025
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