论文标题
一维剂量量子晶格系统阶段的分类
A classification of phases of bosonic quantum lattice systems in one dimension
论文作者
论文摘要
我们研究一维胸腔量子晶格系统的可逆状态。我们表明，每个可逆的1D状态都处于微不足道的阶段：张开了一些未渗透的Ancillas后，它可以通过有限深度量子电路的模糊类似物来解散。如果可逆状态具有对称性，那么即使在添加了未输入的Ancillas之后，也可能不可能以保持对称性的方式将其拆开。我们表明，在有限的统一对称性G的情况下，唯一的障碍物是$ g $的第二学位共同体中价值的指数。我们表明，当且仅当它们的指数重合时，两个可逆$ g $ invariant的状态处于同一阶段。
We study invertible states of 1d bosonic quantum lattice systems. We show that every invertible 1d state is in a trivial phase: after tensoring with some unentangled ancillas it can be disentangled by a fuzzy analog of a finite-depth quantum circuit. If an invertible state has symmetries, it may be impossible to disentangle it in a way that preserves the symmetries, even after adding unentagled ancillas. We show that in the case of a finite unitary symmetry G the only obstruction is an index valued in degree-2 cohomology of $G$. We show that two invertible $G$-invariant states are in the same phase if and only if their indices coincide.
