渗流作为$\mathbb{Z}_2$格点规范理论中的禁闭序参量
Percolation as a confinement order parameter in $\mathbb{Z}_2$ lattice gauge theories
AI总结：
本文提出受渗流启发的序参量POPs，通过量子模拟器的电场基快照探测$\mathbb{Z}_2$格点规范理论中的禁闭，并结合经典分析与量子Monte Carlo揭示其相图和临界指数。
摘要：
格点规范理论（LGTs）由Wilson于1974年提出，用于研究夸克禁闭。这些模型已被证明表现出（退）禁闭相，但定义实验上可获取的序参量仍然具有挑战性。在此，我们提出受渗流启发的序参量（POPs），利用量子模拟器可获取的电场基快照，探测$\mathbb{Z}_2$ LGTs中动力学物质的禁闭。我们将POPs应用于研究一个经典$\mathbb{Z}_2$ LGT，并发现在二维中，对于任意非零密度的$\mathbb{Z}_2$电荷，直到温度$T=\infty$都存在禁闭相（在三维中存在临界$T_c$，即有限温度相变）。此外，利用量子Monte Carlo，我们证明POPs在$T=0$时重现方格Fradkin-Shenker相图，并探索$T>0$时的相图。相关长度指数与三维Ising普适类的指数一致，并且我们确定了表征渗流的POP临界指数。我们提出的POPs提供了禁闭的几何视角，并且可直接从量子模拟器获得的快照中获取，使其适合作为量子自旋液体的探针。
英文摘要：
Lattice gauge theories (LGTs) were introduced in 1974 by Wilson to study quark confinement. These models have been shown to exhibit (de-)confined phases, yet it remains challenging to define experimentally accessible order parameters. Here we propose percolation-inspired order parameters (POPs) to probe confinement of dynamical matter in $\mathbb{Z}_2$ LGTs using electric field basis snapshots accessible to quantum simulators. We apply the POPs to study a classical $\mathbb{Z}_2$ LGT and find a confining phase up to temperature $T=\infty$ in 2D (critical $T_c$, i.e. finite-$T$ phase transition, in 3D) for any non-zero density of $\mathbb{Z}_2$ charges. Further, using quantum Monte Carlo we demonstrate that the POPs reproduce the square lattice Fradkin-Shenker phase diagram at $T=0$ and explore the phase diagram at $T>0$. The correlation length exponent coincides with the one of the 3D Ising universality class and we determine the POP critical exponent characterizing percolation. Our proposed POPs provide a geometric perspective of confinement and are directly accessible to snapshots obtained in quantum simulators, making them suitable as a probe for quantum spin liquids.
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