论文标题
扭曲的边界条件和离散对称性的Lieb-Schultz-Mattis构成性
Twisted boundary condition and Lieb-Schultz-Mattis ingappability for discrete symmetries
论文作者
论文摘要
我们讨论具有晶格翻译和离散现场对称性的量子多体系统。我们指出，在对称操作扭曲的边界条件下，如果单位单元形成现场离散对称性的射击表示，则基态存在确切的变性。基于量子传递矩阵形式主义，我们表明，如果系统陷入困境，则在扭曲边界条件下的地面堕落性也意味着在周期性边界条件下的地面（准）退化。这为最近提议的Lieb-Schultz-Mattis型配置性提供了令人信服的证据，这是由于现场离散对称性在两个和更高维度中的。
We discuss quantum many-body systems with lattice translation and discrete onsite symmetries. We point out that, under a boundary condition twisted by a symmetry operation, there is an exact degeneracy of ground states if the unit cell forms a projective representation of the onsite discrete symmetry. Based on the quantum transfer matrix formalism, we show that, if the system is gapped, the ground-state degeneracy under the twisted boundary condition also implies a ground-state (quasi-)degeneracy under the periodic boundary conditions. This gives a compelling evidence for the recently proposed Lieb-Schultz-Mattis type ingappability due to the onsite discrete symmetry in two and higher dimensions.
