扭曲边界条件下量子相位的平移约束
Translation constraints on quantum phases with twisted boundary conditions
摘要：
量子相位的体性质应该与边界条件的特定选择无关，只要边界尊重对称性。基于这一物理上合理的要求，我们讨论了二维量子磁体中的Lieb-Schultz-Mattis型可吸性，该边界条件使得晶格系统中的量子异常变得明显。特别是，我们直接我们的注意力到棋盘格上的那些密切相关的受抑量子磁铁的正方形晶格和Shastry-Sutherland晶格。我们讨论了在由空间旋转和反射扭曲的边界条件下，绝热U（1）通量通过闭合路径的插入。在这种边界条件下的二维系统有效地放在一个不可定向的空间，即克莱因瓶。我们证明了克莱因瓶空间上的平移对称性排除了唯一的和带隙的基态的可能性。利用磁通插入理论，我们还讨论了棋盘格点上海森堡反铁磁体在磁化平台上的基态简并。
英文摘要：
Bulk properties of quantum phases should be independent of a specific choice of boundary conditions as long as the boundary respects the symmetries. Based on this physically reasonable requirement, we discuss the Lieb-Schultz-Mattis-type ingappability in two-dimensional quantum magnets under a boundary condition that makes evident a quantum anomaly underlying the lattice system. In particular, we direct our attention to those on the checkerboard lattice which are closely related to frustrated quantum magnets on the square lattice and on the Shastry-Sutherland lattice. Our discussion is focused on the adiabatic U(1) flux insertion through a closed path in a boundary condition twisted by a spatial rotation and a reflection. Two-dimensional systems in this boundary condition are effectively put on a nonorientable space, namely the Klein bottle. We show that the translation symmetry on the Klein-bottle space excludes the possibility of the unique and gapped ground state. Taking advantage of the flux insertion argument, we also discuss the ground-state degeneracy on magnetization plateaus of the Heisenberg antiferromagnet on the checkerboard lattice.
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