# Incommmensurability and unconventional superconductor to insulator transition in the Hubbard model with bond-charge interaction

## TL;DR

This paper maps the phase diagram of a 1D Hubbard model with bond-charge interaction, revealing incommensurate superconductivity and multiple phase transitions driven by interaction parameters.

## Contribution

It introduces the phase diagram of the Hubbard model with bond-charge interaction, highlighting a new incommensurate superconductor phase and multiple phase transitions.

## Key findings

- Identification of three distinct phases at large X and positive U.
- Discovery of a novel incommensurate singlet superconductor phase.
- Observation of sequential spin and charge transitions.

## Abstract

We determine the quantum phase diagram of the one-dimensional Hubbard model with bond-charge interaction X in addition to the usual Coulomb repulsion U at half-filling. For large enough X and positive U the model shows three phases. For large U the system is in the spin-density wave phase already known in the usual Hubbard model. As U decreases, there is first a spin transition to a spontaneously dimerized bond-ordered wave phase and then a charge transition to a novel phase in which the dominant correlations at large distances correspond to an incommensurate singlet superconductor.