Localization and topological transitions in non-Hermitian quasiperiodic lattices Article Swipe
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· 2021
· Open Access
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· DOI: https://doi.org/10.1103/physreva.103.033325
· OA: W3118318270
We investigate the localization and topological transitions in a\none-dimensional (interacting) non-Hermitian quasiperiodic lattice, which is\ndescribed by a generalized Aubry-Andr\\'{e}-Harper model with irrational\nmodulations in the off-diagonal hopping and on-site potential and with\nnon-Hermiticities from the nonreciprocal hopping and complex potential phase.\nFor noninteracting cases, we reveal that the nonreciprocal hopping (the complex\npotential phase) can enlarge the delocalization (localization) region in the\nphase diagrams spanned by two quasiperiodical modulation strengths. We show\nthat the localization transition are always accompanied by a topological phase\ntransition characterized the winding numbers of eigenenergies in three\ndifferent non-Hermitian cases. Moreover, we find that a real-complex\neigenenergy transition in the energy spectrum coincides with (occurs before)\nthese two phase transitions in the nonreciprocal (complex potential) case,\nwhile the real-complex transition is absent under the coexistence of the two\nnon-Hermiticities. For interacting spinless fermions, we demonstrate that the\nextended phase and the many-body localized phase can be identified by the\nentanglement entropy of eigenstates and the level statistics of complex\neigenenergies. By making the critical scaling analysis, we further show that\nthe many-body localization transition coincides with the real-complex\ntransition and occurs before the topological transition in the nonreciprocal\ncase, which are absent in the complex phase case.\n
