标题： 异常流入、对偶性和由测量诱导的阿贝尔晶格规范场理论的量子模拟 显示英文标题

标题： Anomaly inflow, dualities, and quantum simulation of abelian lattice gauge theories induced by measurements

摘要： 先前的工作[SciPost Phys. 14, 129 (2023)]已经证明，一般维度下阿贝尔晶格规范理论（包括 Wegner 模型中的 toric code 极限）的量子模拟可以通过作用于具有高阶广义全局对称性的对称保护拓扑（SPT）态上的局部自适应测量来实现。资源 SPT 态的纠缠结构反映了规范理论的几何结构。在这项工作中，我们通过展示由体态测量获得的边界态的异常规范变化与体理论的异常规范变化相匹配，明确展示了被模拟规范理论的脱禁闭相与体内的 SPT 态之间的异常流入机制。此外，我们构建了用于基于测量的量子模拟具有物质场的晶格规范理论（Fradkin-Shenker 模型）的资源态和测量模式，并提出了一种简单方案以保护模拟态的规范不变性免受误差影响。我们进一步考虑了晶格规范理论的资源态波函数与参数化乘积态波函数之间的重叠，并推导出具有插入对应于更高形式全局对称性规范化的缺陷的分区函数之间以及部分重叠所诱导的状态具有不同（对称保护的）拓扑序的测量诱导相之间的精确对偶性。还给出了辅助测量操作以对偶化晶格规范理论的量子哈密顿量及其非可逆性。 显示英文摘要

摘要： Previous work [SciPost Phys. 14, 129 (2023)] has demonstrated that quantum simulation of abelian lattice gauge theories (Wegner models including the toric code in a limit) in general dimensions can be achieved by local adaptive measurements on symmetry-protected topological (SPT) states with higher-form generalized global symmetries. The entanglement structure of the resource SPT state reflects the geometric structure of the gauge theory. In this work, we explicitly demonstrate the anomaly inflow mechanism between the deconfining phase of the simulated gauge theory on the boundary and the SPT state in the bulk, by showing that the anomalous gauge variation of the boundary state obtained by bulk measurement matches that of the bulk theory. Moreover, we construct the resource state and the measurement pattern for the measurement-based quantum simulation of a lattice gauge theory with a matter field (Fradkin-Shenker model), where a simple scheme to protect gauge invariance of the simulated state against errors is proposed. We further consider taking an overlap between the wave function of the resource state for lattice gauge theories and that of a parameterized product state, and we derive precise dualities between partition functions with insertion of defects corresponding to gauging higher-form global symmetries, as well as measurement-induced phases where states induced by a partial overlap possess different (symmetry-protected) topological orders. Measurement-assisted operators to dualize quantum Hamiltonians of lattice gauge theories and their non-invertibility are also presented.