スピンチューブにおける新奇量子相の理論的探究

研究了三角格点上具有SU（N）内自由度的费米子。我们证明了，在每个元格存在π/2人工规范场的情况下，SU（N）对称且每个格点一个粒子的费米子的Mott绝缘相一般具有一个扩展的手征相，该手征相具有内禀拓扑序，其特征在于周期边界条件下的N个低单重激发的多重态，和SU（N）_1 Wess-Zumino-Novikov-Witten共形场论描述的开边界手征边缘态。这是通过对N在3到9之间的严格对角化和基于一组N个Gutzwiller投影的费米波函数的部分子结构实现的，其中每个三角形元格的通量为π/N。随着最近在含费米镱原子的三维光学晶格中实现Mott交叉机制，实验实现强关联SU（N）量子磁性的前景变得光明。我们提出的三角形晶格的基础上已经分别证明的成分：实现莫特绝缘体的光学晶格的可能性，并创建静态人工规范场的光学晶格（碱性原子）。此外，与三角形晶格一起工作是一个很大的优势，因为3-位点置换项是从每个位点一个粒子的Hubbard模型开始的第一个也是唯一一个出现在三阶微扰理论中的项，与例如正方形和蜂窝晶格相比，它们分别出现在4阶和6阶。

We studied fermions with SU(N) internal degrees of freedom on the triangular lattice. .We showed that, in the presence of a pi/2 artificial gauge field per plaquette, Mott insulating phases of fermions with SU(N) symmetry and one particle per site generically possess an extended chiral phase with intrinsic topological order characterized by a multiplet of N low-lying singlet excitations for periodic boundary conditions, and by chiral edge states described by the SU(N)_1 Wess-Zumino-Novikov-Witten conformal field theory for open boundary conditions. This has been achieved by extensive exact diagonalizations for N between 3 and 9, and by a parton construction based on a set of N Gutzwiller projected fermionic wave-functions with flux pi/N per triangular plaquette.With the recent realization of the Mott-crossover regime in 3D optical lattices with fermionic Ytterbium atoms the prospect for the experimental realization of strongly correlated SU(N) quantum magnetism is becoming bright. Our proposal for triangular lattices builds on ingredients which have been demonstrated separately: the possibility to realize Mott insulators in optical lattices, and to create static artificial gauge fields in an optical lattice (for alkaline atoms). Besides, working with the triangular lattice is a big advantage because the 3-site permutation term is the first and only term to appear to third order perturbation theory starting from the Hubbard model with one particle per site, by contrast to e.g. the square and honeycomb lattice, where they appear at order 4 and 6 respectively.