Singularities and Pseudogaps in the Density of States of Peierls Chains

We develop a non-perturbative method to calculate the density of states (DOS) of the fluctuating gap model describing the low-energy physics of electrons on a disordered Peierls chain. For real order parameter field we calculate 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 Peierls order parameter, we show that in the thermodynamic limit the average DOS at the Fermi energy 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.