标题： 在退相干下的二维SPT相的检测 显示英文标题

标题： Detection of 2D SPT phases under decoherence

摘要： 我们提出了一种体订单参数，用于利用部分对称性从二维晶格上的量子多体混合态中提取对称性保护的拓扑（SPT）不变量。 该过程基于作者中的一些人最近开发的部分对称性订单参数，用于研究纯态的SPT相，并将其适应到退相干环境中。 对于一个对称性$G = E \times A$，其中$E$是强对称性，$A$是弱对称性，我们证明部分对称性订单参数可以检测由$E$和$A$联合保护的SPT不变量。 我们通过使用从具有$\mathbb{Z}_2\times\mathbb{Z}_2$对称性的CZX型模型得到的一类混合态，并施加削弱其中一个$\mathbb{Z}_2$对称性的噪声来明确演示这一点。 我们还评论了通过随机测量在量子模拟器中实际检测SPT不变量的问题。 显示英文摘要

摘要： We propose a bulk order parameter for extracting symmetry-protected topological (SPT) invariants of quantum many-body mixed states on a two dimensional lattice using partial symmetries. The procedure builds on the partial symmetry order parameter recently developed by some of the authors to study SPT phases of pure states and adapts them to the decohered setting. For a symmetry $G = E \times A$ where $E$ is a strong symmetry and $A$ is a weak symmetry, we show that the partial symmetry order parameter detects SPT invariants jointly protected by $E$ and $A$. We demonstrate this explicitly using a class of mixed states obtained from CZX-type models with $\mathbb{Z}_2\times\mathbb{Z}_2$ symmetry and subjecting them to noise that weakens one of the $\mathbb{Z}_2$ symmetries. We also comment on the practical detection of SPT invariants in quantum simulators through randomized measurements.