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)内自由度的费米子。我们证明了在每斑块存在一个pi/2的人工规范场的情况下，具有SU(N)对称性和每位点一个粒子的费米子的Mott绝热相一般具有扩展的手性相，其本征拓扑有序在周期边界条件下表现为N个低空单重态的多重激发，在开放边界条件下表现为SU(N)_1 wss - zumino - novikov - witten共形场理论所描述的手性边缘态。这是通过N在3和9之间的广泛精确对角化，以及基于一组N个古茨威勒投影费米子波函数的分子构造实现的，每个三角形斑块的通量为pi/N。随着费米子镱原子三维光学晶格中莫特交叉态的实现，强相关SU(N)量子磁性实验实现的前景变得光明。我们对三角形晶格的建议建立在已经单独证明的成分的基础上：在光学晶格中实现莫特绝缘体的可能性，以及在光学晶格中创建静态人工规范场（用于碱性原子）的可能性。此外，使用三角形晶格是一个很大的优势，因为从哈伯德模型开始，3点排列项是第一个也是唯一一个出现在三阶微扰理论中的项，每个位置有一个粒子，而不是正方形和蜂窝晶格，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.