Quantum frustrated Wigner chains

A Wigner chain in a periodic potential is a paradigmatic example of geometric frustration with long-range interactions. The dynamics emulates the Frenkel-Kontorova model with Coulomb interactions. In the continuum approximation, dislocations are sine-Gordon solitons with power-law decaying tails. We show that their action is mapped into a massive, long-range (1+1) Thirring model, where the solitons are charged fermionic excitations over an effective Dirac sea. We identify the corresponding mean field theory and show that the Coulomb interactions destabilize structures commensurate with the periodic substrate, suppressing their onset and giving rise to {\it interaction-induced} lubrication. Our study identifies the role of long-range interactions on determining nanofriction. Our predictions can be probed in state-of-the-art trapped ion experiments.