Ground-state properties of one-dimensional matter and quantum dissociation of a Luttinger liquid

Abstract

We analyze ground-state properties of strictly one-dimensional molecular matter comprised of identical particles of mass m. Such a class of systems can be described by an additive two-body potential whose functional form is common to all substances which only differ in the energy εand range l scales of the potential. With this choice De Boer's quantum theorem of corresponding states holds thus implying that ground-state properties expressed in appropriate reduced form are only determined by the dimensionless parameter λ_{0}^{2} \sim \hbar^{2}/ml^{2}εmeasuring the strength of zero-point motion in the system. The presence of a minimum in the two-body interaction potential leads to a many-body bound state which is a Luttinger liquid. As λ_{0} increases, the asymmetry of the two-body potential causes quantum expansion, softening, and eventual evaporation of the Luttinger liquid into a gas phase. Selecting the pair interaction potential in the Morse form we analytically compute the properties of the Luttinger liquid and its range of existence. As lambda_{0} increases, the system first undergoes a discontinuous evaporation transition into a diatomic gas followed by a continuous dissociation transition into a monoatomic gas. In particular we find that spin-polarized isotopes of hydrogen and He-3 are monoatomic gases, He-4 is a diatomic gas, while molecular hydrogen and heavier substances are Luttinger liquids. We also investigate the effect of finite pressure on the properties of the liquid and monoatomic gas phases. In particular we estimate a pressure at which molecular hydrogen undergoes an inverse Peierls transition into a metallic state which is a one-dimensional analog of the transition predicted by Wigner and Huntington in 1935.