DNA denaturation as a problem of translational-symmetry restoration

We study the quantum-mechanical version of a model proposed by Peyrard and Bishop [Phys. Rev. Lett. 62, 2755 (1989)] to describe the denaturation phenomenon on the DNA double helix. We characterize denaturation as a phase transition leading to the restoration of the translational invariance of the system. The problem is approached via a modified perturbative theory which incorporates also nonperturbative effects. These are accounted by an auxiliary random variable u describing the equilibrium positions of the constituting particles. The criticality of the model is revealed by analyzing equations involving the first and second cumulants of the u-distribution function. As a consequence, an analytical expression for the critical temperature ${\mathit{T}}_{\mathit{c}}$ is obtained as a function of all model parameters.