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A two-scale effective model for defect-induced localization transitions in non-Hermitian systems (2403.12546v1)
Published 19 Mar 2024 in cond-mat.mes-hall, math-ph, and math.MP
Abstract: We illuminate the fundamental mechanism responsible for the transition between the non-Hermitian skin effect and defect-induced localization in the bulk. We study a Hamiltonian with non-reciprocal couplings that exhibits the skin effect (the localization of all eigenvectors at one edge) and add an on-site defect in the center. Using a two-scale asymptotic method, we characterize the long-scale growth and decay of the eigenvectors and derive a simple and intuitive effective model for the transition that occurs when the defect is sufficiently large that one of the modes is localized at the defect site, rather than at the edge of the system.
- N. Okuma and M. Sato, Non-Hermitian topological phenomena: A review, Ann. Rev. Cond. Mat. Phys. 14, 83 (2023).
- Y. Ashida, Z. Gong, and M. Ueda, Non-Hermitian physics, Adv. Phys. 69, 249 (2020).
- E. J. Bergholtz, J. C. Budich, and F. K. Kunst, Exceptional topology of non-Hermitian systems, Rev. Mod. Phys. 93, 015005 (2021).
- C. M. Bender and S. Boettcher, Real spectra in non-Hermitian Hamiltonians having PT symmetry, Phys. Rev. Lett. 80, 5243 (1998).
- C. M. Bender, Making sense of non-Hermitian Hamiltonians, Rep. Prog. Phys. 70, 947 (2007).
- S. Yao and Z. Wang, Edge states and topological invariants of non-Hermitian systems, Phys. Rev. Lett. 121, 086803 (2018).
- F. Song, S. Yao, and Z. Wang, Non-Hermitian skin effect and chiral damping in open quantum systems, Phys. Rev. Lett. 123, 170401 (2019).
- C. Scheibner, W. T. M. Irvine, and V. Vitelli, Non-Hermitian band topology and skin modes in active elastic media, Phys. Rev. Lett. 125, 118001 (2020).
- C. H. Lee and R. Thomale, Anatomy of skin modes and topology in non-Hermitian systems, Phys. Rev. B 99, 201103 (2019).
- K. Kawabata, M. Sato, and K. Shiozaki, Higher-order non-Hermitian skin effect, Physical Review B 102, 205118 (2020).
- K. Zhang, Z. Yang, and C. Fang, Universal non-Hermitian skin effect in two and higher dimensions, Nat. Commun. 13, 2496 (2022b).
- N. Hatano and D. R. Nelson, Localization transitions in non-Hermitian quantum mechanics, Phys. Rev. Lett. 77, 570 (1996).
- N. Hatano and D. R. Nelson, Non-Hermitian delocalization and eigenfunctions, Phys. Rev. B 58, 8384 (1998).
- P. Brouwer, P. Silvestrov, and C. Beenakker, Theory of directed localization in one dimension, Phys. Rev. B 56, R4333 (1997).
- I. Goldsheid and S. Sodin, Real eigenvalues in the non-Hermitian Anderson model, Ann. Appl. Probab. 28, 3075 (2018).
- S. Longhi, Probing non-Hermitian skin effect and non-Bloch phase transitions, Phys. Rev. Research 1, 023013 (2019).
- D. S. Borgnia, A. J. Kruchkov, and R.-J. Slager, Non-Hermitian boundary modes and topology, Phys. Rev. Lett. 124, 056802 (2020).
- V. M. Martinez Alvarez, J. E. Barrios Vargas, and L. E. F. Foa Torres, Non-Hermitian robust edge states in one dimension: Anomalous localization and eigenspace condensation at exceptional points, Phys. Rev. B 97, 121401 (2018).
- M. Makwana and R. Craster, Localised point defect states in asymptotic models of discrete lattices, Q. J. Mech. Appl. Math. 66, 289 (2013).
- R. V. Craster and B. Davies, Asymptotic characterization of localized defect modes: Su–Schrieffer–Heeger and related models, Multiscale Model. Simul. 21, 827 (2023).
- A. Böttcher and B. Silbermann, Introduction to Large Truncated Toeplitz Matrices (Springer Science & Business Media, New York, 2012).
- L. N. Trefethen and M. Embree, Spectra and Pseudospectra (Princeton University Press, Princeton, NJ, 2005).
- L. Voon and M. Willatzen, The k·p Method (Springer, Berlin, 2009).
- R. V. Craster, J. Kaplunov, and A. V. Pichugin, High-frequency homogenization for periodic media, Proc. R. Soc. A 466, 2341 (2010a).
- G. Allaire, Homogenization and two-scale convergence, SIAM J. Math. Anal. 23, 1482 (1992).
- H. Ammari, H. Lee, and H. Zhang, Bloch waves in bubbly crystal near the first band gap: a high-frequency homogenization approach, SIAM J. Math. Anal. 51, 45 (2019).
- C. Boutin, A. Rallu, and S. Hans, Large scale modulation of high frequency waves in periodic elastic composites, J. Mech. Phys. Solids 70, 362 (2014).
- D. Colquitt, R. V. Craster, and M. Makwana, High frequency homogenisation for elastic lattices, Q. J. Mech. Appl. Math. 68, 203 (2015).
- E. Nolde, R. V. Craster, and J. Kaplunov, High frequency homogenization for structural mechanics, J. Mech. Phys. Solids 59, 651 (2011).
- B. B. Guzina and M. Bonnet, Effective wave motion in periodic discontinua near spectral singularities at finite frequencies and wavenumbers, Wave Motion 103, 102729 (2021).
- B. B. Guzina, S. Meng, and O. Oudghiri-Idrissi, A rational framework for dynamic homogenization at finite wavelengths and frequencies, Proc. R. Soc. A 475, 20180547 (2019).
- J. C. Budich and E. J. Bergholtz, Non-Hermitian topological sensors, Phys. Rev. Lett. 125, 180403 (2020).
- S. Jana and L. Sirota, Tunneling-like wave transmission in non-Hermitian lattices with mirrored nonreciprocity, arXiv preprint arXiv:2312.16182 (2023).
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