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Article Dans Une Revue Physical Review B: Condensed Matter and Materials Physics (1998-2015) Année : 2015

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

Résumé

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−V1−V2 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.
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hal-01223370 , version 1 (21-11-2019)

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Sylvain Capponi, A. M. Läuchli. Phase diagram of interacting spinless fermions on the honeycomb lattice: A comprehensive exact diagonalization study. Physical Review B: Condensed Matter and Materials Physics (1998-2015), 2015, 92 (8), pp.085146. ⟨10.1103/PhysRevB.92.085146⟩. ⟨hal-01223370⟩
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