Observation of topology of non-Hermitian systems without chiral symmetry

doi:10.1088/1674-1056/addcc1

Abstract Topological invariants are crucial for characterizing topological systems. However, experimentally measuring them presents a significant challenge, especially in non-Hermitian systems where the biorthogonal eigenvectors are often necessary. We propose a general approach for measuring the topological invariants of one-dimensional non-Hermitian systems, which can be derived from the spin textures of right eigenstates. By utilizing a dilation method, we realize a non-Hermitian system without chiral symmetry on a two-qubit nuclear magnetic resonance system and measure the winding number associated with the eigenstates. In addition to examining the topology of the eigenstates, our experiment also reveals the topological structure of the energy band, which differs from that in chiral systems. Our work paves the way for further exploration of complex topological properties in non-Hermitian systems without chiral symmetry.

Keywords: nuclear magnetic resonance quantum simulation non-Hermitian system topological phases

Received: 04 April 2025
Revised: 12 May 2025
Accepted manuscript online: 23 May 2025

PACS:	03.67.Lx	(Quantum computation architectures and implementations)
	03.65.Vf	(Phases: geometric; dynamic or topological)
	05.30.Rt	(Quantum phase transitions)
	76.60.-k	(Nuclear magnetic resonance and relaxation)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11805008), Guangdong Basic and Applied Basic Research Foundation (Grant No. 2024A1515011406), the Fundamental Research Funds for the Central Universities, Sun Yat-Sen University (Grant No. 23qnpy63), and the Fund from Guangdong Provincial Key Laboratory (Grant No. 2019B121203005).

Corresponding Authors: Zhihuang Luo
E-mail: luozhih5@mail.sysu.edu.cn

Cite this article:

Shuo Wang(王硕), Zhengjie Kang(康正杰), Hao Li(李浩), Jiaojiao Li(李姣姣) Yuanjie Zhang(张元杰), and Zhihuang Luo(罗智煌) Observation of topology of non-Hermitian systems without chiral symmetry 2025 Chin. Phys. B 34 110304

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Observation of topology of non-Hermitian systems without chiral symmetry

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