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Spontaneous Chern-Euler Duality Transitions

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arxiv 2503.21861 v1 pith:SVJFF44J submitted 2025-03-27 cond-mat.mes-hall math-phmath.MPphysics.opticsquant-ph

Kang Yang , Zhi Li , Peng Xue , Emil J. Bergholtz , Piet W. Brouwer This is my paper
classification cond-mat.mes-hallmath-phmath.MPphysics.opticsquant-ph
keywords transitionsnumbersymmetrytopologicalbandschangesdualityfeatures
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Topological phase transitions are typically characterized by abrupt changes in a quantized invariant. Here we report a contrasting paradigm in non-Hermitian parity-time symmetric systems, where the topological invariant remains conserved, but its nature transitions between the Chern number, characteristic of chiral transport in complex bands, and the Euler number, which characterizes the number of nodal points in pairs of real bands. The transition features qualitative changes in the non-Abelian geometric phases during spontaneous parity-time symmetry breaking, where different quantized components become mutually convertible. Our findings establish a novel topological duality principle governing transitions across symmetry classes and reveal unique non-unitary features intertwining topology, symmetry, and non-Abelian gauge structure.

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Cited by 3 Pith papers

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