论文标题
具有较高对称性在一般维度的系统的广泛光谱退化的定理
A Theorem on Extensive Spectral Degeneracy for Systems with Higher Symmetries in General Dimensions
论文作者
论文摘要
我们本着Lieb-Schultz-Mattis定理的精神建立了具有较高（仪表类似）对称性的量子系统的频谱退化，并在任意数量的空间维度中具有相当通用的物理边界条件。与应用扭曲或同等绝热操作相反，我们利用了修改的边界条件的影响。当边界几何形状的一般选择在接近热力学极限时无关紧要时，表现出像对称性（例如轨道指南针模型）这样的非交通仪的系统必须具有每个光谱水平的指数（边界大小）变性。我们简要讨论为什么由于与红外脱光化的混合相关的经过证实的大堕落性，但由于熵“按疾病的“订单”类型效应），某些系统仍然可能表现出常规的物理行为，即具有非扩展归化的系统的系统行为。
We establish, in the spirit of the Lieb-Schultz-Mattis theorem, lower bounds on the spectral degeneracy of quantum systems with higher (Gauge Like) symmetries with rather generic physical boundary conditions in an arbitrary number of spatial dimensions. Contrary to applying twists or equivalent adiabatic operations, we exploit the effects of modified boundary conditions. When a general choice of boundary geometry is immaterial in approaching the thermodynamic limit, systems that exhibit non-commuting Gauge Like symmetries, such as the orbital compass model, must have an exponential (in the size of the boundary) degeneracy of each of their spectral levels. We briefly discuss why, in spite of the proven large degeneracy associated with infrared-ultraviolet mixing, some systems may still exhibit conventional physical behaviors, i.e., of those of systems with non-extensive degeneracies, due to entropic "order by disorder" type effects.
