Statistical thermodynamics of anharmonic carbon chains

We develop an analytical and self-consistent thermodynamic model for carbyne using the unsymmetrized self-consistent field theory. By deriving closed-form expressions for the Helmholtz and Gibbs free energies, as well as vibrational and response functions, we analyze the temperature dependence of self-consistent potentials and one-particle distributions. Our results demonstrate that quantum and classical anharmonicities reshape the effective potential landscape, driving spontaneous symmetry breaking and a thermodynamic phase transition from cumulene to polyyne. The resulting analytical phase diagram reveals how thermal effects govern the structural stability of one-dimensional carbon chains.