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

Abstract

Motivated by emerging experimental possibilities to confine atoms and molecules in quasi-one-dimensional geometries, 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 $\ensuremath{\epsilon}$ and range l scales of the potential. With this choice De Boer's quantum theorem of corresponding states holds and the ground-state properties expressed in appropriate reduced form are only determined by the dimensionless parameter ${\ensuremath{\lambda}}_{0}^{2}\ensuremath{\sim}{\ensuremath{\Elzxh}}^{2}{/ml}^{2}\ensuremath{\epsilon},$ measuring 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 stable for not very large ${\ensuremath{\lambda}}_{0}.$ As ${\ensuremath{\lambda}}_{0}$ 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. We find that as ${\ensuremath{\lambda}}_{0}$ 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 ${}^{3}\mathrm{He}$ are monoatomic gases, ${}^{4}\mathrm{He}$ 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 [E. Wigner and H.B. Huntington, J. Chem Phys. 3, 764 (1935)].