Incipient quantum melting of the one-dimensional Wigner lattice

TL;DR

This paper investigates the quantum melting process of a one-dimensional Wigner lattice by analyzing the energy of kink-antikink pairs in a tight-binding model with long-range Coulomb interactions, revealing the critical Coulomb strength for melting.

Contribution

It provides a theoretical analysis of the incipient quantum melting of the 1D Wigner lattice through exact solutions for kink-antikink pairs at specific fillings.

Findings

Pair energy becomes negative at a critical Coulomb strength V_c/t≈s^3.

The negative pair energy indicates the onset of quantum melting.

The study identifies the relationship between Coulomb strength and lattice stability.

Abstract

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 $n=1/s$, where $s$ is an integer larger than 1. The pair energy becomes negative for a relatively high value of $V$, $V_c/t\approx s^3$. This signals the initial stage of the quantum melting of the Wigner lattice.