Singularities and pseudogaps in the density of states of Peierls chains

We develop a nonperturbative method to calculate the density of states (DOS) rho(omega) of the fluctuating gap model describing the low-energy physics of electrons on a disordered Peierls chain. For a real order parameter field we calculate rho(0) (i.e., the DOS at the Fermi energy) exactly as a functional of the disorder for a chain of finite length L. Averaging rho(0) with respect to a Gaussian probability distribution of the fluctuating Peierls order parameter, we show that for L --> infinity the average [rho(0)] diverges for any finite value of the correlation length above the Peierls transition. Pseudogap behavior emerges only if the Peierls order parameter is finite and sufficiently large.