Exact Mobility Edges in a Disorder-Free Dimerized Stark Lattice with Effective Unbounded Hopping

• URL: http://arxiv.org/abs/2601.02259v2
• Date: Tue, 06 Jan 2026 16:40:26 GMT
• Title: Exact Mobility Edges in a Disorder-Free Dimerized Stark Lattice with Effective Unbounded Hopping
• Authors: Yunyao Qi, Heng Lin, Quanfeng Lu, Dong Ruan, Gui-Lu Long,
• Abstract summary: A disorder-free one-dimensional single-particle Hamiltonian hosts an exact mobility edge (ME)<n>We analytically derive the bulk spectrum in reciprocal space, identifying a sharp ME where the energy magnitude equals the inter-cell hopping strength.<n>Our numerical results indicate that the ME is robust against potential experimental imperfections.
• Score: 3.638953299008847
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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