一维相互作用系统中基态的子系统保真度
Sub-system fidelity for ground states in one dimensional interacting systems
摘要：
我们提出利用子系统保真度（SSF）来识别和/或表征一维相互作用多体系统中的对称性保护拓扑（SPT）态，SSF是通过比较一对从简并基态导出的约化密度矩阵来定义的. SSF通过给定子系统内的测量来判断两个状态是否是局部不可区分的（LI）。从两个极态（可以在任一边缘区分的状态）开始，这些状态的其他组合可以映射到布洛赫球上。我们证明了Bloch球赤道上的一对正交态是LI，与它们是SPT态还是猫态（由打破离散对称性的状态的线性组合得到的保序态）无关。有了这个定理，我们提供了一个计划，以构建零能量激发交换的LI状态。我们发现，零模可以位于任何地方的猫状态，但本地化的边缘附近的SPT状态。我们还表明，SPT状态是LI在一个有限的分数的散装（不包括两个边缘），而碎核状态是可区分的。这可以用于精确定位从SPT状态到中断状态的转变。
英文摘要：
We propose to utilize the sub-system fidelity (SSF), defined by comparing a pair of reduced density matrices derived from the degenerate ground states, to identify and/or characterize symmetry protected topological (SPT) states in one-dimensional interacting many-body systems. The SSF tells whether two states are locally indistinguishable (LI) by measurements within a given sub-system. Starting from two polar states (states that could be distinguished on either edge), the other combinations of these states can be mapped onto a Bloch sphere. We prove that a pair of orthogonal states on the equator of the Bloch sphere are LI, independently of whether they are SPT states or cat states (symmetry-preserving states by linear combinations of states that break discrete symmetries). Armed with this theorem, we provide a scheme to construct zero-energy exitations that swap the LI states. We show that the zero mode can be located anywhere for cat states, but is localized near the edge for SPT states. We also show that the SPT states are LI in a finite fraction of the bulk (excluding the two edges), whereas the symmetry-breaking states are distinguishable. This can be used to pinpoint the transition from SPT states to the symmetry-breaking states.
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