Absence of Mobility Edge in Short-range Uncorrelated Disordered Model: Coexistence of Localized and Extended States
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866929218764406784 |
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| author | Das, Adway Kumar Ghosh, Anandamohan Khaymovich, Ivan M. |
| author_facet | Das, Adway Kumar Ghosh, Anandamohan Khaymovich, Ivan M. |
| contents | Unlike the well-known Mott's argument that extended and localized states should not coexist at the same energy in a generic random potential, we provide an example of a nearest-neighbor tight-binding disordered model which carries both localized and extended states without forming the mobility edge (ME). Unexpectedly, this example appears to be given by a well-studied $β$-ensemble with independently distributed random diagonal potential and inhomogeneous kinetic hopping terms. In order to analytically tackle the problem, we locally map the above model to the 1D Anderson model with matrix-size- and position-dependent hopping and confirm the coexistence of localized and extended states, which is shown to be robust to the perturbations of both potential and kinetic terms due to the separation of the above states in space. In addition, the mapping shows that the extended states are non-ergodic and allows to analytically estimate their fractal dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_02351 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Absence of Mobility Edge in Short-range Uncorrelated Disordered Model: Coexistence of Localized and Extended States Das, Adway Kumar Ghosh, Anandamohan Khaymovich, Ivan M. Disordered Systems and Neural Networks Other Condensed Matter Quantum Physics Unlike the well-known Mott's argument that extended and localized states should not coexist at the same energy in a generic random potential, we provide an example of a nearest-neighbor tight-binding disordered model which carries both localized and extended states without forming the mobility edge (ME). Unexpectedly, this example appears to be given by a well-studied $β$-ensemble with independently distributed random diagonal potential and inhomogeneous kinetic hopping terms. In order to analytically tackle the problem, we locally map the above model to the 1D Anderson model with matrix-size- and position-dependent hopping and confirm the coexistence of localized and extended states, which is shown to be robust to the perturbations of both potential and kinetic terms due to the separation of the above states in space. In addition, the mapping shows that the extended states are non-ergodic and allows to analytically estimate their fractal dimensions. |
| title | Absence of Mobility Edge in Short-range Uncorrelated Disordered Model: Coexistence of Localized and Extended States |
| topic | Disordered Systems and Neural Networks Other Condensed Matter Quantum Physics |
| url | https://arxiv.org/abs/2305.02351 |