Truncation-dependent PT phase transition for the edge states of a two-dimensional non-Hermitian system
Abstract
We consider a bulk system supporting parity and time reversal ($PT$) symmetry, and investigate how the $PT$ phase transition of edge states is influenced by different truncations of the system. As an example, we study a two-dimensional $PT$-symmetric Su--Schrieffer--Heeger lattice with non-Hermitian onsite potentials. We find that when the truncation preserves certain symmetries of the bulk lattice, the edge states can remain in the $PT$-unbroken phase when the non-Hermitian onsite potentials are less than a nonzero critical value. On the other hand, when the truncation removes such symmetries, edge states with complex eigen-energies are observed for infinitesimal non-Hermitian onsite potentials. We develop an analytic theory to account for such behaviors. Our results are important in the manipulation of the gain and loss behaviors of edge states in non-Hermitian systems, with potential applications in the study of topological lasers, quantum sensors, and unidirectional invisibility.
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While a linear dispersion can be synthesized at Γ point in time-reversal-invariant systems, there always exist additional flat bands, and such linear dispersions are accidental.
“While a linear dispersion can be synthesized at Γ point in time-reversal-invariant systems, there always exist additional flat bands [49][50][51], and such linear dispersions are accidental.”
From Non-Abelian lattice gauge fields in photonic synthetic frequency dimensions (2025) · cites this paper as [50]
Cites
Observation of topological edge states in parity–time-symmetric quantum walks
Xiao, L., Zhan, X., Bian, Z. H., Wang, K. K., Zhang, X., Wang, X. P., Li, J., Mochizuki, K., Kim, D., Kawakami, N., et al. (2017) · Nature Physics · doi:10.1038/nphys4204 · Cited by 576 · see citing works
Quantum walks on a programmable two-dimensional 62-qubit superconducting processor
Gong, M., Wang, S., Zha, C., Chen, M.-C., Huang, H.-L., Wu, Y., Zhu, Q., Zhao, Y., Li, S., Guo, S., et al. (2021) · Science · doi:10.1126/science.abg7812 · Cited by 331 · see citing works
Fractional Bloch oscillations in photonic lattices
Corrielli, G., Crespi, A., Della Valle, G., Longhi, S., & Osellame, R. (2013) · Nature Communications · doi:10.1038/ncomms2578 · Cited by 173 · see citing works
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Non-Abelian lattice gauge fields in photonic synthetic frequency dimensions
Cheng, D., Wang, K., Roques-Carmes, C., Lustig, E., Long, O. Y., Wang, H., & Fan, S. (2025) · Nature · doi:10.1038/s41586-024-08259-2 · Cited by 58 · see citing works
Self-citation
- Authors
- Cheng, D., Peng, B., Xiao, M., Chen, X., Yuan, L., & Fan, S.
- Affiliations
- Shanghai Jiao Tong University (CN)
- Wuhan University (CN)
- Stanford University (US)
- Venue
- Physical Review B
- Publisher
- American Physical Society (APS)
- Published
- 2022-05-06
- Volume
- 105
- Issue
- 20
- ISSN
- 2469-9950 (ISSN-L)
- 2469-9969
- OpenAlex
- W4229002111
- Cited by
- 17
- References
- 3
- Citations by year
- 2026: 2 · 2025: 3 · 2024: 6 · 2023: 3 · 2022: 3
- FWCI
- 1.54
- Type
- journal article
- Language
- en
- Open access
- closed
- Licence
- Locations
- Physical review. B./Physical review. B (publishedVersion)
- Funders
- National Natural Science Foundation of China (12122407, 11974245)
- National Basic Research Program of China (2017YFA0303701)
- Science and Technology Commission of Shanghai Municipality (2019SHZDZX01)
- Natural Science Foundation of Shanghai (19ZR1475700)
- Program for Professor of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning
- U.S. Department of Defense (N00014-17-1-3030)
- Simons Foundation (827065)
- Shandong Quancheng Scholarship (00242019024)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Non-Hermitian Physics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Topological Materials and Phenomena
- Physical Sciences › Mathematics › Mathematical Physics › Spectral Theory in Mathematical Physics
- Keywords
- PT symmetry, PT phase transition, edge states, non-Hermitian systems, truncation effects, Su-Schrieffer-Heeger lattice, complex eigenvalues, gain and loss, topological lasers, unidirectional invisibility, two-dimensional lattice
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