Finite-size effects and quantum phonon fluctuations in the optical absorption edgeof dimerized chains

We study effects of quantum phonons on the optical conductivity σ(ω) for finite dimerized chains by using two numerical methods: exact numerical diagonalization and by factorizing the electron-phonon wave function (AA, adiabatic ansatz). For small chains, we compare the results of these methods and find a criterion for a valid AA. AA turns out to be: (a) a substantial improvement with respect to the adiabatic approximation usually employed in condensed-matter physics, and (b) much less affected by computer storage limitations than exact diagonalization. We use AA and get σ(ω) reliably for sufficiently large chains, which could be realized experimentally. The optical gap as well as the σ(ω) curve near the absorption edge possess a surprisingly strong dependence on the chain size; this could be relevant for experiments on mesoscopic systems.