Superconductivity and Topological Numbers in the Hubbard Chain with Bond-Charge Interaction

TL;DR

This paper maps out the complex phase diagram of a Hubbard chain with bond-charge interaction, revealing various phases and topological transitions relevant to certain organic compounds.

Contribution

It introduces a detailed analysis combining geometric and continuum field theory methods to identify topological quantum phase transitions in this model.

Findings

Multiple insulating, metallic, and superconducting phases identified.

Charge and spin gaps closing as topological transitions via Berry phase jumps.

Ground-state displacement operator characterizes phase nature.

Abstract

We determine the quantum phase diagram of the Hubbard chain with electron-hole symmetric correlated hopping at 1/2- and 1/4-filling using geometric concepts and continuum limit field theory. The long distance behavior of various correlation functions show a very rich phase diagram with several insulating, metallic, and superconducting phases, which might be relevant to (TMTSF)$_2$X compounds. The closing of charge and spin gaps are accurately resolved as topological transitions (jumps in $\pi$ of Berry phases). The metallic or insulating character of each thermodynamic phase is obtained from the ground-state expectation value of a displacement operator in reciprocal space.