Exact Mobility Edges in a Disorder-Free Dimerized Stark Lattice with Effective Unbounded Hopping
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866912989639081984 |
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| author | Qi, Yunyao Lin, Heng Lu, Quanfeng Ruan, Dong Long, Gui-Lu |
| author_facet | Qi, Yunyao Lin, Heng Lu, Quanfeng Ruan, Dong Long, Gui-Lu |
| contents | We propose a disorder-free one-dimensional single-particle Hamiltonian hosting an exact mobility edge (ME), placing the system outside the assumptions of no-go theorems regarding unbounded potentials. By applying a linear Stark potential selectively to one sublattice of a dimerized chain, we generate an effective Hamiltonian with unbounded, staggered hopping amplitudes. The unbounded nature of the hopping places the model outside the scope of the Simon-Spencer theorem, while the staggered scaling allows it to evade broader constraints on Jacobi matrices. We analytically derive the bulk spectrum in reciprocal space, identifying a sharp ME where the energy magnitude equals the inter-cell hopping strength. This edge separates a continuum of extended states from two distinct localized branches: a standard unbounded Wannier-Stark ladder and an anomalous bounded branch accumulating at the ME. The existence of extended states is supported by finite-size scaling of the inverse participation ratio up to system sizes $L \sim 10^9$. Furthermore, we propose an experimental realization using photonic frequency synthetic dimensions. Our numerical results indicate that the ME is robust against potential experimental imperfections, including frequency detuning errors and photon loss, establishing a practical path for observing MEs in disorder-free systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_02259 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Exact Mobility Edges in a Disorder-Free Dimerized Stark Lattice with Effective Unbounded Hopping Qi, Yunyao Lin, Heng Lu, Quanfeng Ruan, Dong Long, Gui-Lu Disordered Systems and Neural Networks Quantum Physics We propose a disorder-free one-dimensional single-particle Hamiltonian hosting an exact mobility edge (ME), placing the system outside the assumptions of no-go theorems regarding unbounded potentials. By applying a linear Stark potential selectively to one sublattice of a dimerized chain, we generate an effective Hamiltonian with unbounded, staggered hopping amplitudes. The unbounded nature of the hopping places the model outside the scope of the Simon-Spencer theorem, while the staggered scaling allows it to evade broader constraints on Jacobi matrices. We analytically derive the bulk spectrum in reciprocal space, identifying a sharp ME where the energy magnitude equals the inter-cell hopping strength. This edge separates a continuum of extended states from two distinct localized branches: a standard unbounded Wannier-Stark ladder and an anomalous bounded branch accumulating at the ME. The existence of extended states is supported by finite-size scaling of the inverse participation ratio up to system sizes $L \sim 10^9$. Furthermore, we propose an experimental realization using photonic frequency synthetic dimensions. Our numerical results indicate that the ME is robust against potential experimental imperfections, including frequency detuning errors and photon loss, establishing a practical path for observing MEs in disorder-free systems. |
| title | Exact Mobility Edges in a Disorder-Free Dimerized Stark Lattice with Effective Unbounded Hopping |
| topic | Disordered Systems and Neural Networks Quantum Physics |
| url | https://arxiv.org/abs/2601.02259 |