Incipient quantum melting of the one-dimensional Wigner lattice

A one–dimensional tight–binding model of electrons with long–range Coulomb interactions is studied in the limit where double site occupancy is forbidden and the Coulomb coupling strength $V$ is large with respect to the hopping amplitude $t$. The quantum problem of a kink–antikink pair generated in the Wigner lattice (the classical ground state for $t=0$) is solved for fillings $n=1\mathrm{/}s$, where $s$ is an integer larger than 1. The pair energy becomes negative for a relatively high value of $V$, $V_c\mathrm{/}t\approx s^3$. This signals the initial stage of the quantum melting of the Wigner lattice.