We study the boundary physics of bulk insulators by considering three coupled Hubbard chains in a linear confining potential. In the Hartree-Fock approximation, the ground state at and slightly off the particle-hole symmetric point remains insulating even at large slopes of the confining potential. By contrast, accounting for quantum fluctuations and correlations through a combination of bosonization and RG methods, we find that there is always a gapless dipole mode, but it does not contribute to a finite compressibility. Moreover, when increasing the slope of the confining potential at half filling, we find a quantum phase transition between an insulating and a metallic state, indicating the formation of a soft edge state of non-topological origin. Away from half filling, a similar transition takes place.
@article{arxiv.2202.04374,
title = {Metal-insulator transition in a boundary three chain model},
author = {Niels John and Yuval Gefen and Bernd Rosenow},
journal= {arXiv preprint arXiv:2202.04374},
year = {2022}
}