Phase Diagrams from Topological Transitions: The Hubbard Chain with Correlated Hopping

TL;DR

This paper maps the quantum phase diagram of the Hubbard chain with correlated hopping using topological invariants, revealing phases analogous to those in organic conductors, and confirming their properties through numerical and symmetry analyses.

Contribution

It introduces a method to determine phase diagrams via topological charge and spin Berry phase jumps, and identifies phase similarities with real materials.

Findings

Charge and spin gaps confirmed by correlation functions

Identification of spin Peierls, SDW, and triplet superconductor phases

Topological transitions correspond to phase boundaries

Abstract

The quantum phase diagram of the Hubbard chain with correlated hopping is accurately determined through jumps in $\pi$ in the charge and spin Berry phases. The nature of each thermodynamic phase, and the existence of charge and spin gaps, is confirmed by calculating correlation functions and other fundamental quantities using numerical methods, and symmetry arguments. Remarkably we find striking similarities between the stable phases for moderate on-site Coulomb repulsion: spin Peierls, spin-density-wave and triplet superconductor, and those measured in (TMTSF)$_2$X.