Quantum metal-insulator transition at half-filling

For the Su-Schrieffer-Heeger-Hubbard model with spin-1/2 electrons at half- filling, we show that there is a metal-insulator transition when both the p honon and electron fluctuations are taken into account. At anti-adiabatic l imit, the transition happens at U/t(0) = 2 pi lambda, where lambda is the d imension-less e-p coupling constant.