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arXiv:0909.5161 · New Journal of Physics

Topological phase transitions in the non-Abelian honeycomb lattice

A. Bermúdez, Nathan Goldman, A. Kubasiak, Maciej Lewenstein, Miguel Angel Martin-Delgado

Published Mar 24, 2010• 79 citations
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Abstract

Ultracold Fermi gases trapped in honeycomb optical lattices provide an intriguing scenario, where relativistic quantum electrodynamics (QED) can be tested. Here, we generalize this system to non-Abelian QED, where massless Dirac fermions interact with effective non-Abelian gauge fields. We show how in this setup a variety of topological phase transitions occur, which arise due to massless fermion pair production events, as well as pair annihilation events of two kinds: spontaneous and strongly interacting induced. Moreover, such phase transitions can be controlled and characterized in optical lattice experiments.

DOI
10.1088/1367-2630/12/3/033041

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Ultracold Fermi gases trapped in honeycomb optical lattices provide an intriguing scenario, where relativistic quantum electrodynamics (QED) can be tested. Here, we generalize this system to non-Abelian QED, where massless Dirac fermions interact with effective non-Abelian gauge fields. We show how in this setup a variety of topological phase transitions occur, which arise due to massless fermion pair production events, as well as pair annihilation events of two kinds: spontaneous and strongly interacting induced. Moreover, such phase transitions can be controlled and characterized in optical lattice experiments.
We study the properties of an ultracold Fermi gas loaded in an optical square lattice and subjected to an external and classical non-Abelian gauge field. We show that this system can be exploited as an optical analogue of relativistic quantum electrodynamics, offering a remarkable route to access the exotic properties of massless Dirac fermions with cold atoms experiments. In particular, we show that the underlying Minkowski space-time can also be modified, reaching anisotropic regimes where a remarkable anomalous quantum Hall effect and a squeezed Landau vacuum could be observed.
The method of synthetic gauge potentials opens up a new avenue for our understanding and discovering novel quantum states of matter. We investigate the topological quantum phase transition of Fermi gases trapped in a honeycomb lattice in the presence of a synthetic non-Abelian gauge potential. We develop a systematic fermionic effective field theory to describe a topological quantum phase transition tuned by the non-Abelian gauge potential and explore its various important experimental consequences. Numerical calculations on lattice scales are performed to compare with the results achieved by the fermionic effective field theory. Several possible experimental detection methods of topological quantum phase transition are proposed. In contrast to condensed matter experiments where only gauge invariant quantities can be measured, both gauge invariant and non-gauge invariant quantities can be measured by experimentally generating various non-Abelian gauges corresponding to the same set of Wilson loops.
Dirac points lie at the heart of many fascinating phenomena in condensed matter physics, from massless electrons in graphene to the emergence of conducting edge states in topological insulators. At a Dirac point, two energy bands intersect linearly and the particles behave as relativistic Dirac fermions. In solids, the rigid structure of the material sets the mass and velocity of the particles, as well as their interactions. A different, highly flexible approach is to create model systems using fermionic atoms trapped in an optical lattice, a method which so far has only been applied to explore simple lattice structures. In my talk I will report on the creation of Dirac points with adjustable properties in a tunable honeycomb optical lattice [1]. Using momentum-resolved interband transitions, we observe a minimum band gap inside the Brillouin zone at the position of the Dirac points. We exploit the unique tunability of our lattice potential to adjust the effective mass of the Dirac fermions by breaking the inversion symmetry of the lattice. Moreover, changing the lattice anisotropy allows us to move the position of the Dirac points inside the Brillouin zone. When increasing the anisotropy beyond a critical limit, the two Dirac points merge and annihilate each other. We map out this topological transition in lattice parameter space and find excellent agreement with ab initio calculations. Our results not only pave the way to model materials where the topology of the band structure plays a crucial role, but also provide the possibility to explore many-body phases resulting from the interplay of complex lattice geometries with interactions.
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.
We study the properties of an ultracold Fermi gas loaded in a square optical lattice and subjected to an external and classical non-Abelian gauge field. We calculate the energy spectrum of the system and show that the Dirac points in the energy spectrum will remain quite stable under on-site interaction of certain strength. Once the on-site interaction grows stronger than a critical value, the Dirac points will no longer be stable and merge into a single hybrid point. This merging implies a quantum phase transition from a semimetallic phase to a band insulator. The on-site interaction between ultracold fermions could be conveniently controlled by Feshbach resonances in current experiments. We propose that this interaction-induced merging of Dirac points may be observed in the ultracold-Fermi-gas experiments.
We investigate the interacting Dirac fermions on honeycomb lattice by cluster dynamical mean-field theory (DMFT) combined with continuous-time quantum Monte Carlo simulation. A novel scenario for the semimetal-Mott insulator transition of the interacting Dirac fermions is found beyond the previous DMFT studies. Our results suggest that for weak interaction, the system is semimetal and the Fermi velocity keeps constant. The system undergoes a second-order Mott transition with increasing the interaction strength. We demonstrate that the nonlocal spatial correlations play a vital role in the Mott transition on the honeycomb lattice. A phase diagram of Mott transition is presented. We also elaborate the experimental protocol to observe this phase transition by the ultracold atoms on optical honeycomb lattice.