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arXiv:1204.4791 · Europhysics Letters (EPL)

Comment on “Topological quantum phase transitions of attractive spinless fermions in a honeycomb lattice” by Poletti D. et al.

Philippe Corboz, Sylvain Capponi, Andreas Martin Läuchli, Bela Bauer, Román Orús

Published Apr 1, 2012• 10 citations
arXivHTMLPDF

Abstract

In a recent letter [D. Poletti et al., EPL 93, 37008 (2011)] a model of attractive spinless fermions on the honeycomb lattice at half filling has been studied by mean-field theory, where distinct homogenous phases at rather large attraction strength $V>3.36$, separated by (topological) phase transitions, have been predicted. In this comment we argue that without additional interactions the ground states in these phases are not stable against phase separation. We determine the onset of phase separation at half filling $V_{ps}\approx 1.7$ by means of infinite projected entangled-pair states (iPEPS) and exact diagonalization.

DOI
10.1209/0295-5075/98/27005

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In a recent letter [D. Poletti et al., EPL 93, 37008 (2011)] a model of attractive spinless fermions on the honeycomb lattice at half filling has been studied by mean-field theory, where distinct homogenous phases at rather large attraction strength V>3.36V>3.36V>3.36, separated by (topological) phase transitions, have been predicted. In this comment we argue that without additional interactions the ground states in these phases are not stable against phase separation. We determine the onset of phase separation at half filling Vps≈1.7V_{ps}\approx 1.7Vps​≈1.7 by means of infinite projected entangled-pair states (iPEPS) and exact diagonalization.
We investigate the phase diagram of spinless fermions with nearest- and next-nearest-neighbor 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 zigzag phase, and a charge ordered state with a 12-site unit cell we call N\'eel domain wall crystal, as well as a region of phase separation for attractive interactions. A sizable 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 noninteracting situation. While for the studied $t\ensuremath{-}{V}_{1}\ensuremath{-}{V}_{2}$ 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.
We investigate a spinless Fermi gas trapped in a honeycomb optical lattice with attractive nearest-neighbor interactions. At zero temperature, the mean-field theory predicts three quantum phase transitions, two being topological. At low interactions, the system is semi-metallic. Increasing the interaction further, the semi-metal destabilizes into a fully gapped superfluid. At larger interactions, a topological transition occurs and this superfluid phase becomes gapless, with Dirac-like dispersion relations. Finally, increasing again the interaction, a second topological transition occurs and the gapless superfluid is replaced by a different fully gapped superfluid phase. We analyze these different quantum phases as the temperature and the lattice filling are varied.
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 nontopological 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.
Attractive interaction between spinless fermions in a two-dimensional lattice drives the formation of a topological superfluid. But the topological phase is dynamically unstable towards phase separation when the system has a high density of states and large interaction strength. This limits the critical temperature to an experimentally challenging regime where, for example, even ultracold atoms and molecules in optical lattices would struggle to realize the topological superfluid. We propose that the introduction of a weaker longer-range repulsion, in addition to the short-range attraction between lattice fermions, will suppress the phase separation instability. Taking the honeycomb lattice as an example, we use the unrestricted Hartree-Fock approximation to show that our proposal significantly enlarges the stable portion of the topological superfluid phase and increases the critical temperature by an order of magnitude. Our work opens a route to enhance the stability of topological superfluids by engineering interparticle interactions.
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We consider extended Hubbard models with repulsive interactions on a honeycomb lattice, and the transitions from the semimetal to Mott insulating phases at half-filling. Because of the frustrated nature of the second-neighbor interactions, topological Mott phases displaying the quantum Hall and the quantum spin Hall effects are found for spinless and spin fermion models, respectively. The mean-field phase diagram is presented and the fluctuations are treated within the random phase approximation. Renormalization group analysis shows that these states can be favored over the topologically trivial Mott insulating states.