Spontaneous Chern-Euler Duality Transitions

Abstract:Topological phase transitions are typically characterized by abrupt changes in a quantized invariant. Here we report a contrasting paradigm in spontaneous parity-time symmetry-breaking transitions induced by non-Hermiticity. 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. This conserved morphing of topological properties applies to all pairs of bands whose spectral gaps to other bands remain open during the transition. It features qualitative changes in the non-Abelian geometric phases, which quantize in different forms across the transition. Our findings establish a generic topological duality principle governing transitions across symmetry classes and reveal unique connections among topology, symmetry, and non-Abelian gauge structure in non-unitary processes.

Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Mathematical Physics (math-ph); Optics (physics.optics); Quantum Physics (quant-ph)

arXiv:2503.21861 [cond-mat.mes-hall]

(or arXiv:2503.21861v2 [cond-mat.mes-hall] for this version)

https://doi.org/10.48550/arXiv.2503.21861 Focus to learn more arXiv-issued DOI via DataCite

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