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arXiv:1006.3179 · Europhysics Letters (EPL)

Topological quantum phase transitions of attractive spinless fermions in a honeycomb lattice

Dario Poletti, Christian Miniatura, Benoît Grémaud

Published Feb 1, 2011• 18 citations
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Abstract

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.

DOI
10.1209/0295-5075/93/37008

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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.
Abstract. We study the superfluid properties of attractively interacting fermions hopping in a family of 2D and 3D lattices in the presence of synthetic gauge fields having pi-flux per plaquette. The reason for such a choice is that the pi-flux cubic lattice displays Dirac points and that decreasing the hopping coefficient in a spatial direction (say, tz) these Dirac points are unaltered: it is then possible to study the 3D-2D interpolation towards the pi-flux square lattice. We also consider the lattice configuration providing the continuous interpolation between the 2D pi-flux square lattice and the honeycomb geometry. We investigate by a mean field analysis the effects of interaction and dimensionality on the superfluid gap, chemical potential and critical temperature, showing that these quantities continuously vary along the patterns of interpolation. In the two-dimensional cases at zero temperature and at half filling there is a quantum phase transition occurring at a critical (negative) interaction Uc presenting a linear critical exponent for the gap as a function of |U − Uc|. We show that in three dimensions this quantum phase transition is again retrieved, pointing out that the critical exponent for the gap changes from 1 to 1/2 for each finite value of tz. ar X iv
We study the attractive fermionic Hubbard model on a honeycomb lattice using determinantal quantum Monte Carlo simulations. By increasing the interaction strength UUU (relative to the hopping parameter ttt) at half filling and zero temperature, the system undergoes a quantum phase transition at 5.0<Uc/t<5.15.0<{U}_{c}/t<5.15.0<Uc​/t<5.1 from a semimetal to a phase displaying simultaneously superfluid behavior and density order. Doping away from half filling, and increasing the interaction strength at finite but low temperature TTT, the system always appears to be a superfluid exhibiting a crossover between a BCS and a molecular regime. These different regimes are analyzed by studying the spectral function. The formation of pairs and the emergence of phase coherence throughout the sample are studied as UUU is increased and TTT is lowered.
We study the superfluid properties of attractively interacting fermions hopping in a family of 2D and 3D lattices in the presence of synthetic gauge fields having π-flux per plaquette. The reason for such a choice is that the π-flux cubic lattice displays Dirac points and that decreasing the hopping coefficient in a spatial direction (say, t z ), these Dirac points are unaltered: it is then possible to study the 3D–2D interpolation towards the π-flux square lattice. We also consider the lattice configuration providing the continuous interpolation between the 2 D π-flux square lattice and the honeycomb geometry. We investigate by a mean-field analysis the effects of interaction and dimensionality on the superfluid gap, chemical potential and critical temperature, showing that these quantities continuously vary along the patterns of interpolation. In the two-dimensional cases at zero temperature and half-filling, there is a quantum phase transition occurring at a critical (negative) interaction U c presenting a linear critical exponent for the gap as a function of | U − U c |. We show that in three dimensions, this quantum phase transition is again retrieved, pointing out that the critical exponent for the gap changes from 1 to 1/2 for each finite value of t z .
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.
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.
Using determinant quantum Monte Carlo simulations, we demonstrate that an extended Hubbard model on a bilayer honeycomb lattice has two novel quantum phase transitions. The first is a quantum phase transition between the weakly interacting gapless Dirac fermion phase and a strongly interacting fully gapped and symmetric trivial phase, which cannot be described by the standard Gross-Neveu model. The second is a quantum critical point between a quantum spin Hall insulator with spin Sz{S}^{z}Sz conservation and the previously mentioned strongly interacting fully gapped phase. At the latter quantum critical point the single-particle excitations remain gapped, while spin and charge gaps both close. We argue that the first quantum phase transition is related to the Z16{\mathbb{Z}}_{16}Z16​ classification of the topological superconductor $^{3}\mathrm{He}\text{\ensuremath{-}}B$ phase with interactions, while the second quantum phase transition is a topological phase transition described by a bosonic O(4)O(4)O(4) nonlinear sigma model field theory with a $\ensuremath{\Theta}$ term.