Peierls instability of a one-dimensional quantum liquid

Whether Peierls distortion occurs for a system of one-dimensional spinless fermions is determined by the exponent g that characterizes the decay of correlations among the electrons in the undistorted state. Noninteracting electrons (g=1) is the marginal case, for which the Peierls effect just barely occurs. For repulsive interactions between the electrons (g<1) the instability is enhanced and the leading dependence of the ground-state energy E on the lattice distortion δ is E∝-δ(Formula presented). For attractive interactions (g≳1) a continuous phase transition between a normal metal and a Peierls insulator takes place for sufficiently strong electron-ion interaction.