Yao, S. & Wang, Z. Edge states and topological invariants of non-Hermitian systems. Phys. Rev. Lett. 121, 086803 (2018).
Google Scholar
Yao, S., Song, F. & Wang, Z. Non-hermitian Chern bands. Phys. Rev. Lett. 121, 136802 (2018).
Google Scholar
Kunst, F. K., Edvardsson, E., Budich, J. C. & Bergholtz, E. J. Biorthogonal bulk-boundary correspondence in non-Hermitian systems. Phys. Rev. Lett. 121, 026808 (2018).
Google Scholar
Yokomizo, K. & Murakami, S. Non-Bloch band theory of non-Hermitian systems. Phys. Rev. Lett. 123, 066404 (2019).
Google Scholar
Guo, S., Dong, C., Zhang, F., Hu, J. & Yang, Z. Theoretical prediction of a non-Hermitian skin effect in ultracold-atom systems. Phys. Rev. A 106, L061302 (2022).
Google Scholar
Zhou, L., Li, H., Yi, W. & Cui, X. Engineering non-Hermitian skin effect with band topology in ultracold gases. Commun. Phys. 5, 252 (2022).
Google Scholar
Li, H. & Yi, W. Dissipative two-dimensional Raman lattice. Phys. Rev. A 107, 013306 (2023).
Google Scholar
Wang, S.-X. & Wan, S. Duality between the generalized non-Hermitian Hatano-Nelson model in flat space and a Hermitian system in curved space. Phys. Rev. B 106, 075112 (2022).
Google Scholar
Ju, C.-Y. et al. Einstein’s quantum elevator: Hermitization of non-Hermitian Hamiltonians via a generalized vielbein formalism. Phys. Rev. Res. 4, 023070 (2022).
Google Scholar
Chenwei, L., Ren, Z., Zhengzheng, Z. & Qi, Z. Curving the space by non-Hermiticity. Nat. Commun. 13, 2184 (2022).
Google Scholar
Ryo, O., Ryo, T. & Kazuki, Y. Second-order topological non-Hermitian skin effects. Phys. Rev. B 102, 241202 (2020).
Google Scholar
Kohei, K., Masatoshi, S. & Ken, S. Higher-order non-Hermitian skin effect. Phys. Rev. B 102, 205118 (2020).
Google Scholar
Ikhlef, Y., Jacobsen, J. L. & Saleur, H. Integrable spin chain for the SL(2, R)/U(1) black hole sigma model. Phys. Rev. Lett. 108, 081601 (2012).
Google Scholar
Bijan, B. & Sauvik, S. Artificial Hawking radiation, weak pseudo-Hermiticity, and Weyl semimetal blackhole analogy. J. Math. Phys. 63, 122102 (2022).
Google Scholar
Ashida, Y., Gong, Z. & Ueda, M. Non-hermitian physics. Adv. Phys. 69, 249–435 (2020).
Google Scholar
El-Ganainy, R. et al. Non-Hermitian physics and PT symmetry. Nat. Phys. 14, 11–19 (2018).
Google Scholar
Helbig, T. et al. Generalized bulk-boundary correspondence in non-Hermitian topolectrical circuits. Nat. Phys. 16, 747–750 (2020).
Google Scholar
Ezawa, M. Non-Hermitian higher-order topological states in nonreciprocal and reciprocal systems with their electric-circuit realization. Phys. Rev. B 99, 201411 (2019).
Google Scholar
Zhou, H. et al. Observation of bulk Fermi arc and polarization half charge from paired exceptional points. Science 359, 1009–1012 (2018).
Google Scholar
Ghatak, A., Brandenbourger, M., Van Wezel, J. & Coulais, C. Observation of non-Hermitian topology and its bulk-edge correspondence in an active mechanical metamaterial. Proc. Natl Acad. Sci. USA 117, 29561 (2020).
Google Scholar
Liu, S. et al. Non-Hermitian skin effect in a non-Hermitian electrical circuit. Research 2021, 5608038 (2021).
Google Scholar
Kozii, V. & Fu, L. Non-Hermitian topological theory of finite-lifetime quasiparticles: Prediction of bulk Fermi arc due to exceptional point. Phys. Rev. B 109, 235139 (2024).
Google Scholar
Shen, H., Zhen, B. & Fu, L. Topological band theory for non-Hermitian Hamiltonians. Phys. Rev. Lett. 120, 146402 (2018).
Google Scholar
Öztürk, F. E. et al. Observation of a non-Hermitian phase transition in an optical quantum gas. Science 372, 88–91 (2021).
Google Scholar
Bergholtz, E. J., Budich, J. C. & Kunst, F. K. Exceptional topology of non-Hermitian systems. Rev. Mod. Phys. 93, 015005 (2021).
Google Scholar
Kawabata, K., Shiozaki, K., Ueda, M. & Sato, M. Symmetry and topology in non-Hermitian physics. Phys. Rev. X 9, 041015 (2019).
Google Scholar
Zhang, K., Yang, Z. & Fang, C. Universal non-Hermitian skin effect in two and higher dimensions. Nat. Commun. 13, 2496 (2022).
Google Scholar
Liang, Q. et al. Dynamic signatures of non-Hermitian skin effect and topology in ultracold atoms. Phys. Rev. Lett. 129, 070401 (2022).
Google Scholar
Weidemann, S. et al. Topological funneling of light. Science 368, 311–314 (2020).
Google Scholar
Xiao, L. et al. Non-Hermitian bulk-boundary correspondence in quantum dynamics. Nat. Phys. 16, 761–766 (2020).
Google Scholar
Nobuyuki, O., Kohei, K., Ken, S. & Masatoshi, S. Topological origin of non-Hermitian skin effects. Phys. Rev. Lett. 124, 086801 (2020).
Google Scholar
Yang, Z., Zhang, K., Fang, C. & Hu, J. Non-Hermitian bulk-boundary correspondence and auxiliary generalized Brillouin zone theory. Phys. Rev. Lett. 125, 226402 (2020).
Google Scholar
Hofmann, T. et al. Reciprocal skin effect and its realization in a topolectrical circuit. Phys. Rev. Res. 2, 023265 (2020).
Google Scholar
Zhang, W. et al. Observation of non-Hermitian aggregation effects induced by strong interactions. Phys. Rev. B 105, 195131 (2022).
Google Scholar
Zou, D. et al. Observation of hybrid higher-order skin-topological effect in non-Hermitian topolectrical circuits. Nat. Commun. 12, 7201 (2021).
Google Scholar
Shang, C. et al. Experimental identification of the second-order non-Hermitian skin effect with physics-graph-informed machine learning. Adv. Sci. 9, 2202922 (2022).
Google Scholar
Zhang, X., Tian, Y., Jiang, J.-H., Lu, M.-H. & Chen, Y.-F. Observation of higher-order non-Hermitian skin effect. Nat. Commun. 12, 5377 (2021).
Google Scholar
Zhou, Q. et al. Observation of geometry-dependent skin effect in non-Hermitian phononic crystals with exceptional points. Nat. Commun. 14, 4569 (2023).
Google Scholar
Wang, W., Hu, M., Wang, X., Ma, G. & Ding, K. Experimental realization of geometry-dependent skin effect in a reciprocal two-dimensional lattice. Phys. Rev. Lett. 131, 207201 (2023).
Google Scholar
Wan, T., Zhang, K., Li, J., Yang, Z. & Yang, Z. Observation of the geometry-dependent skin effect and dynamical degeneracy splitting. Sci. Bull. 68, 2330–2335 (2023).
Google Scholar
Gopalakrishnan, S. & Gullans, M. J. Entanglement and purification transitions in non-Hermitian quantum mechanics. Phys. Rev. Lett. 126, 170503 (2021).
Google Scholar
Okuma, N. & Sato, M. Quantum anomaly, non-Hermitian skin effects, and entanglement entropy in open systems. Phys. Rev. B 103, 085428 (2021).
Google Scholar
Kawabata, K., Numasawa, T. & Ryu, S. Entanglement phase transition induced by the non-Hermitian skin effect. Phys. Rev. X 13, 021007 (2023).
Google Scholar
Song, B. et al. Observation of symmetry-protected topological band with ultracold fermions. Sci. Adv. 4, eaao4748 (2018).
Google Scholar
Liu, X.-J., Liu, Z.-X. & Cheng, M. Manipulating topological edge spins in a one-dimensional optical lattice. Phys. Rev. Lett. 110, 076401 (2013).
Google Scholar
Ren, Z. et al. Chiral control of quantum states in non-Hermitian spin-orbit-coupled fermions. Nat. Phys. 18, 385–389 (2022).
Google Scholar
Zhang, K., Yang, Z. & Fang, C. Correspondence between winding numbers and skin modes in non-Hermitian systems. Phys. Rev. Lett. 125, 126402 (2020).
Google Scholar
Liu, X.-J., Law, K. T. & Ng, T. K. Realization of 2D spin-orbit interaction and exotic topological orders in cold atoms. Phys. Rev. Lett. 112, 086401 (2014).
Google Scholar
Song, B. et al. Observation of nodal-line semimetal with ultracold fermions in an optical lattice. Nat. Phys. 15, 911–916 (2019).
Google Scholar
Liang, M.-C. et al. Realization of Qi-Wu-Zhang model in spin-orbit-coupled ultracold fermions. Phys. Rev. Res. 5, L012006 (2023).
Google Scholar
Zhen, B. et al. Spawning rings of exceptional points out of Dirac cones. Nature 525, 354–358 (2015).
Google Scholar
Yi, Y. & Yang, Z. Non-Hermitian skin modes induced by on-site dissipations and chiral tunneling effect. Phys. Rev. Lett. 125, 186802 (2020).
Google Scholar
Wang, H.-Y., Song, F. & Wang, Z. Amoeba formulation of non-Bloch band theory in arbitrary dimensions. Phys. Rev. X 14, 021011 (2024).
Google Scholar
Zhang, K., Yang, Z. & Sun, K. Edge theory of non-Hermitian skin modes in higher dimensions. Phys. Rev. B 109, 165127 (2024).
Google Scholar
Asteria, L., Zahn, H. P., Kosch, M. N., Sengstock, K. & Weitenberg, C. Quantum gas magnifier for sub-lattice-resolved imaging of 3D quantum systems. Nature 599, 571–575 (2021).
Google Scholar
Wang, Z. Y., Hong, J. S. & Liu, X. J. Symmetric non-Hermitian skin effect with emergent nonlocal correspondence. Phys. Rev. B 108, L060204 (2023).
Google Scholar
Kaluza, T. On the unification problem in physics. Int. J. Mod. Phys. D 27, 1870001 (2018).
Google Scholar
Klein, O. Quantentheorie und fünfdimensionale Relativitätstheorie. Z. Phys. 37, 895–906 (1926).
Google Scholar
Klein, O. The atomicity of electricity as a quantum theory law. Nature 118, 516 (1926).
Google Scholar
Song, B. et al. Spin-orbit-coupled two-electron Fermi gases of ytterbium atoms. Phys. Rev. A 94, 061604 (2016).
Google Scholar
Murthy, P. et al. Matter-wave Fourier optics with a strongly interacting two-dimensional Fermi gas. Phys. Rev. A 90, 043611 (2014).
Google Scholar
Holten, M. et al. Observation of Cooper pairs in a mesoscopic two-dimensional Fermi gas. Nature 606, 287–291 (2022).
Google Scholar
Mao, L., Deng, T. & Zhang, P. Boundary condition independence of non-Hermitian Hamiltonian dynamics. Phys. Rev. B 104, 125435 (2021).
Google Scholar
