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The European Physical Journal B

Dynamical quantum phase transition in the non-Hermitian generalized Su–Schrieffer–Heeger model

Jiawen Yao, Ruohan Zhang, Siyuan Cheng, Zhengling WANG, Haoran Gu

Published Jun 1, 2026• 0 citations
Publisher
DOI
10.1140/epjb/s10051-026-01186-3

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We demonstrate that genuinely non-Hermitian topological phases and corresponding topological phase transitions can be naturally realized in monitored quantum circuits, exemplified by the paradigmatic non-Hermitian Su-Schrieffer-Heeger model.We emulate this model by a 1D chain of spinless electrons evolving under unitary dynamics and subject to periodic measurements that are stochastically invoked.The non-Hermitian topology is visible in topological invariants adapted to the context of monitored circuits.For instance, the topological phase diagram of the monitored realization of the non-Hermitian Su-Schrieffer-Heeger model is obtained from the biorthogonal polarization computed from an effective Hamiltonian of the monitored system.Importantly, our monitored circuit realization allows direct access to steady-state biorthogonal expectation values of generic observables, and hence, to measure physical properties of a genuine non-Hermitian model.We expect our results to be applicable more generally to a wide range of models that host non-Hermitian topological phases.
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.