We propose a minimal two-leg ladder model in which the mobility edge (ME) arises solely from bond modulation, induced by a slowly varying quasiperiodic modulation of the interleg tunneling amplitudes. We demonstrate that this bond-modulated ladder naturally hosts two propagation channels, whose symmetric and antisymmetric combinations experience opposite effective on-site potentials. Using the adiabatic (slowly varying) limit of the modulation, we derive an exact analytical condition for the single-particle mobility edge, $E_c=\pm |2t-\lambda |,$ where $t$ is the hopping amplitude along both legs and $\lambda$ is the bond modulation strength. This result directly generalizes the classic ME condition for slowly varying on-site potentials to a multileg (two-leg in our case) geometry. Extensive numerical calculations, including inverse participation ratios, Lyapunov exponents, density of states, and participation-ratio scaling, demonstrate excellent agreement with the analytical prediction across a wide range of parameters. We further identify a regime for small modulation exponents $0<\nu <1$, where localized and weakly delocalized states coexist even beyond the transition point $({\lambda }_c=2t)$. Finally, we characterize the crossover from the slowly varying regime to a true quasiperiodic regime where the adiabatic approximation breaks down, supported by a thorough scaling analysis of the generalized participation ratio and the multifractal properties of the eigenstates. Our results establish that a deterministic bond modulation can serve as a sufficient ingredient to produce an exact ME in ladder systems, offering experimentally accessible and advantageous routes toward tuning nonergodic extended phases.

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• Localization
• 1-dimensional systems
• Transfer matrix calculations