Novel quantum mechanism with SU(2N) Hubbard model


Slater v.s. Mott: novel quantum magnetism of SU(2N) fermions

There exist two basic pictures for interacting insulators -- the weak coupling Slater mechanism based on Fermi surface nesting, and the strong coupling Mott one based on local moments and super-exchange. In the SU(2) case, the evolution between these two limits is smooth without a quantum phase transition.

How about in the SU(2N) case? We have found fundamentally different features by the sign-problem free QMC based on SU(2N) Hubbard models on the square lattice [Ref. 1] . The AFM order appears in weak and intermediate coupling regions agreeing with the Slater insulator picture. However, as further increasing interaction, it becomes suppressed. In the SU(6) case, the AFM is completely suppressed in the strong interacting region, i.e., the Mott insulator, where the quantum paramagnetic columnar dimer state appears. This shows a clear quantum phase transition between the Slater and Mott insulating regions.

Novel quantum phase transitions of the SU(2N) Dirac fermions

We investigated the Mott-insulating state of the SU(2N) Dirac fermions via the sign-problem free QMC simulations [Ref. 2 ] . It is based on the SU(2N) Hubbard model on a honeycomb lattice. Unlike the SU(2) case, the SU(4) and SU(6) Mott-insulating phases are identified with the columnar valence-bond-solid (cVBS) order in the absence of the Neel ordering. Although the Dirac semimetal-to-cVBS transitions are typically first order due to a cubic invariance possessed by the cVBS order, the coupling to gapless Dirac fermions can soften these transitions to the second order at zero temperature.

Interaction Effects with Varying N in SU(N) Symmetric Fermion Lattice Systems

The interaction effects in ultracold Fermi gases with SU(N) symmetry are studied nonperturbatively in half filled one-dimensional lattices by employing quantum Monte Carlo simulations Ref. [3]. We find that, as N increases, weak and strong interacting systems are driven to a crossover region, but from opposite directions as a convergence of itinerancy and Mottness. In the weak interaction region, particles are nearly itinerant, and interparticle collisions are enhanced by N, resulting in the amplification of interaction effects. In contrast, in the strong coupling region, increasing N softens the Mott-insulating background through the enhanced virtual hopping processes. The crossover region exhibits nearly N-independent physical quantities, including the relative bandwidth, Fermi distribution, and the spin structure factor. The difference between even-N and odd-N systems is most prominent at small N's with strong interactions, since the odd case allows local real hopping with an energy scale much larger than the virtual one. The above effects can be experimentally tested in ultracold atom experiments with alkaline-earth(-like) fermions such as 87Sr (173 Yb).

References and Talks

  • 1. Da Wang, Yi Li, Zi Cai, Zhichao Zhou, Yu Wang, Congjun Wu, Competing orders in the 2D half-filled SU(2N) Hubbard model through the pinning field quantum Monte-Carlo simulations
    Phys. Rev. Lett. 112, 156403 (2014), See pdf file

  • 2. Zhichao Zhou, Da Wang, Zi Yang Meng, Yu Wang, Congjun Wu , Mott insulating states and quantum phase transitions of correlated SU(2N) Dirac fermions
    Phys. Rev. B 93, 245157 (2016)     . See pdf file

  • 3. Shenglong Xu, Julio Barreiro, Yu Wang, Congjun Wu, "Interaction effects from the parity of N in SU(N) symmetric fermion lattice systems",
    Phys. Rev. Lett. 121, 167205 (2018)     , see pdf file

  • Talk Slater and Mott Physics with SU(N) Hubbard models .

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    Last modified: 2018.