Quantum one-dimensional materials at low temperature: Pre-critical effects, long-range correlations, and specific heats

In 1925, Ising showed that a one-dimensional (1D) system of particles that interact with short-range intermolecular forces cannot exhibit a phase transition at finite temperatures. However, he also found that the correlation length ξ diverges to infinity at T = 0 K and low density, the signature of a critical point. In this work, we report classical and quantum mechanical path integral Monte Carlo (PIMC) results for the static pair correlation function, the correlation length, and specific heats for a 1D system of spin 0 Lennard-Jones (LJ) molecules modeled on hydrogen, H2. Our PIMC results, which are for temperatures down to T* = kBT/ɛ = 0.01 and densities down to ρ* = ρσ = 0.1, exhibit strong long-range fluctuations out to 50 molecular diameters or more at low temperatures and low densities. In addition, the correlation length appears to diverge as the temperature approaches 0 K, thus strongly confirming Ising's prediction of a critical point at T = 0 K. Our classical Monte Carlo results, by contrast, show smaller values of the correlation length, since it does not capture the quantum dispersion effect. The specific heat at constant length is also found to diverge on lowering the temperature toward absolute zero, a further signature of the approach to a critical point, but the third law of thermodynamics requires that it drop to zero at a temperature that is below the lowest value studied in this work. The findings reported here are relevant to recent advances in the synthesis of one-dimensional van der Waals materials.