Metal-insulator transition in a boundary three chain model

TL;DR

This paper investigates the boundary physics of bulk insulators using a three coupled Hubbard chains model, revealing a quantum phase transition from insulator to metal driven by the confining potential slope.

Contribution

It combines bosonization and RG methods to show the existence of a gapless mode and identifies a non-topological quantum phase transition at the boundary.

Findings

Insulating ground state remains stable at and near particle-hole symmetry in Hartree-Fock approximation.

Quantum fluctuations induce a gapless dipole mode that does not affect compressibility.

A quantum phase transition from insulator to metal occurs with increasing confining potential slope.

Abstract

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.