スピンチューブにおける新奇量子相の理論的探究

我们研究了三角晶格上具有SU(N)内部自由度的费米子。结果表明，在每个斑块存在pi/2人工规范场的情况下，具有SU(N)对称性且每个格点只有一个粒子的费米子的Mott绝缘相一般具有内禀拓扑序，其特征为周期边界条件下的N个低位单重态激发和开放边界条件下的SU(N)_1Wess-Zumino-Novikov-Witten共形场理论所描述的手征边态。这是通过N在3到9之间广泛的精确对角化，以及基于一组N个古兹威尔投影的费米子波函数的部分子构造实现的，每个三角格子的通量pi/N。随着最近费米子Yb原子在三维光学晶格中实现Mott交叉区域，强关联SU(N)量子磁性的实验实现的前景变得光明起来。我们关于三角形晶格的提议建立在已经分别证明的成分的基础上：在光学晶格中实现Mott绝缘体的可能性，以及在光学晶格中(对于碱性原子)创建静态人工规范场的可能性。此外，使用三角形晶格是一个很大的优势，因为三位置换项是第一个也是唯一一个出现在三阶微扰理论中的项，它始于每位点一个粒子的Hubbard模型，而不是例如方形和蜂窝晶格，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.