Scaling Properties of Energy Gap in Dimerized Spinless Fermion Chains with Quasiperiodic Modulation

By employing the exact diagonalization method, we investigate the low-energy behaviour of the dimerized spinless fermion chains with quasiperiodic modulation. It is found that for off-diagonal modulation, the energy gap with length N scales as exp(-cN^ω) with nonuniversal exponent ω if the dimerization is nonzero. However, for diagonal modulation, there may exist a critical dimerization δ_c beyond which the system exhibits a metal--insulator transition.