Phase diagram of interacting spinless fermions on the honeycomb lattice: A comprehensive exact diagonalization study

TL;DR

This study maps the phase diagram of spinless fermions on a honeycomb lattice using exact diagonalization, revealing various charge-ordered phases, classical degeneracies, and exploring the potential for a topological Mott insulator.

Contribution

First comprehensive exact diagonalization analysis of the full Hamiltonian for spinless fermions on the honeycomb lattice, identifying multiple charge-ordered phases and examining topological phases.

Findings

Identified several charge-ordered phases including Néel, zig-zag, and Néel domain wall crystal.

Found evidence for a Kekulé or plaquette bond-order wave phase at intermediate interactions.

Did not find conclusive evidence for a topological Mott insulator in the studied model.

Abstract

We investigate the phase diagram of spinless fermions with nearest and next-nearest neighbour density-density interactions on the honeycomb lattice at half-filling. Using Exact Diagonalization techniques of the full Hamiltonian and constrained subspaces, combined with a careful choice of finite-size clusters, we determine the different charge orderings that occur for large interactions. In this regime we find a two-sublattice N\'eel-like state, a charge modulated state with a tripling of the unit cell, a zig-zag phase and a novel charge ordered states with a 12 site unit cells we call N\'eel domain wall crystal, as well as a region of phase separation for attractive interactions. A sizeable region of the phase diagram is classically degenerate, but it remains unclear whether an order-by-disorder mechanism will lift the degeneracy. For intermediate repulsion we find evidence for a Kekul\'e or plaquette bond-order wave phase. We also investigate the possibility of a spontaneous Chern insulator phase (dubbed topological Mott insulator), as previously put forward by several mean-field studies. Although we are unable to detect convincing evidence for this phase based on energy spectra and order parameters, we find an enhancement of current-current correlations with the expected spatial structure compared to the non-interacting situation. While for the studied $t{-}V_1{-}V_2$ model the phase transition to the putative topological Mott insulator is preempted by the phase transitions to the various ordered states, our findings might hint at the possibility for a topological Mott insulator in an enlarged Hamiltonian parameter space, where the competing phases are suppressed.