Interaction driven phases in the half-filled honeycomb lattice: an infinite density matrix renormalization group study

TL;DR

This study uses infinite density matrix renormalization group methods to clarify the phase diagram of the half-filled honeycomb lattice, finding no evidence for the topological Chern insulator phase and identifying new charge-ordered phases.

Contribution

The paper provides the first comprehensive numerical analysis supporting the absence of the Chern insulator phase and reveals two new charge-ordered phases in the model.

Findings

No Chern insulator phase detected.

Discovery of two new charge-ordered phases.

Confirmation of non-topological orders previously identified.

Abstract

The emergence of the Haldane Chern insulator state due to strong short range repulsive interactions in the half-filled fermionic spinless honeycomb lattice model has been proposed and challenged with different methods and yet it still remains controversial. In this work we revisit the problem using the infinite density matrix renormalization group method and report numerical evidence supporting i) the absence of the Chern insulator state, ii) two previously unnoticed charge ordered phases and iii) the existence and stability of all the non-topological competing orders that were found previously within mean field. In addition, we discuss the nature of the corresponding phase transitions based on our numerical data. Our work establishes the phase diagram of the half-filled honeycomb lattice model tilting the balance towards the absence of a Chern insulator phase for this model.