Measuring topological invariants of even-dimensional non-Hermitian systems through quench dynamics

• URL: http://arxiv.org/abs/2505.23633v3
• Date: Wed, 04 Jun 2025 14:12:11 GMT
• Title: Measuring topological invariants of even-dimensional non-Hermitian systems through quench dynamics
• Authors: Xiao-Dong Lin, Long Zhang,
• Abstract summary: Non-Hermitian (NH) topological invariants play a central role in the study of NH topological phases.<n>We propose a general framework for directly measuring NH topological invariants in even-dimensional systems.<n>We show that NH topological invariants can be extracted from the winding patterns of a dynamical field constructed from post-quench spin textures.
• Score: 6.33906375869588
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The accurate determination of non-Hermitian (NH) topological invariants plays a central role in the study of NH topological phases. In this work, we propose a general framework for directly measuring NH topological invariants in even-dimensional systems through quench dynamics. Our approach hinges on constructing an auxiliary Hermitian matrix topologically equivalent to the original NH Hamiltonian, enabling topological characterization via reduced-dimensional momentum subspaces called band inversion surfaces (BISs). A key insight lies in the emergence of chiral symmetry in the NH Hamiltonian specifically on BISs -- a critical property that allows extension of the dynamical characterization scheme previously developed for odd-dimensional NH systems with chiral or sublattice symmetry [Lin et al., Phys. Rev. Res. 7, L012060 (2025)]. We show that NH topological invariants can be extracted from the winding patterns of a dynamical field constructed from post-quench spin textures on BISs. We demonstrate our approach through a detailed analysis of NH Chern insulators and then extend the framework to higher even-dimensional systems by introducing second-order BISs for characterization. This work establishes an experimentally accessible protocol for detecting NH topological invariants in quantum platforms.

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