论文标题
用非反对矩阵的产品操作员对称量子状态
Gauging quantum states with non-anomalous matrix product operator symmetries
论文作者
论文摘要
测量系统的全球对称性等同于引入新的自由度，其转换规则使整个系统观察到了局部对称性。在量子系统中，可能会有障碍物来衡量全球对称性。发生这种情况时，对称性被称为异常。这样的障碍与以下事实有关，即不能将全球对称性写成本地运营商的张量产物。在本手稿中，我们研究具有附加结构的非本地对称性：它们采用矩阵产品运算符（MPO）的形式。我们利用MPO的张量网络结构来构建满足相同组关系的本地操作员，也就是说，我们能够本地化异常的MPO。对于非反对MPO，我们使用这些局部操作员明确评估获得非平凡测量状态的一维量子状态的MPO对称性。我们表明，我们的测量程序像标准现场情况一样满足所有所需的属性。我们还展示了该过程如何在由MPO对称性保护的基质产品状态中自然表示。在异常MPO的情况下，我们阐明了衡量这些对称性的障碍物。
Gauging a global symmetry of a system amounts to introducing new degrees of freedom whose transformation rule makes the overall system observe a local symmetry. In quantum systems there can be obstructions to gauging a global symmetry. When this happens the symmetry is dubbed anomalous. Such obstructions are related to the fact that the global symmetry cannot be written as a tensor product of local operators. In this manuscript we study non-local symmetries that have an additional structure: they take the form of a matrix product operator (MPO). We exploit the tensor network structure of the MPOs to construct local operators from them satisfying the same group relations, that is, we are able to localize even anomalous MPOs. For non-anomalous MPOs, we use these local operators to explicitly gauge the MPO symmetry of a one-dimensional quantum state obtaining non-trivial gauged states. We show that our gauging procedure satisfies all the desired properties as the standard on-site case does. We also show how this procedure is naturally represented in matrix product states protected by MPO symmetries. In the case of anomalous MPOs, we shed light on the obstructions to gauging these symmetries.
