标题： 真实$2+1$D弦在量子模拟器中的平面项作用 显示英文标题

标题： Role of Plaquette Term in Genuine $2+1$D String Dynamics on Quantum Simulators

摘要： 随着量子模拟器在$2+1$维格点规范理论 (LGTs) 的出现，一个基本的开放性问题是，在什么情况下观察到的物理现象是真正属于$2+1$维而不是有效属于$1+1$维。在这里，我们针对在当前努力将字符串动力学在$2+1$维 LGTs 上进行量子模拟的问题进行探讨。通过张量网络模拟和分析推导，我们表明，表示磁场的平面项仅在$d>1$个空间维度中出现，并在禁闭区域深处对\textit{真正的} $2+1$ 维字符串动力学起着关键作用。 在缺乏的情况下，对于最短长度（曼哈顿距离）的字符串，我们展示了如何将字符串断裂，尽管是在$d=2$维空间晶格中，可以有效地映射到一个与晶格几何无关的$1+1$D 动态过程。 我们的发现不仅回答了什么是真正的$2+1$D 字符串动力学的问题，还为未来$2+1$D LGTs 的量子模拟实验提供了明确的指导。 显示英文摘要

摘要： With the advent of quantum simulators of $2+1$D lattice gauge theories (LGTs), a fundamental open question is under what circumstances the observed physics is genuinely $2+1$D rather than effectively $1+1$D. Here, we address this question in the ongoing strong effort to quantum-simulate string dynamics in $2+1$D LGTs on state-of-the-art quantum hardware. Through tensor network simulations and analytic derivations, we show that the plaquette term, which represents a magnetic field and only emerges in $d>1$ spatial dimensions, plays a crucial role in \textit{genuine} $2+1$D string dynamics deep in the confined regime. In its absence and for minimal-length (Manhattan-distance) strings, we demonstrate how string breaking, although on a lattice in $d=2$ spatial dimensions, can be effectively mapped to a $1+1$D dynamical process independently of lattice geometry. Our findings not only answer the question of what qualifies as genuine $2+1$D string dynamics, but also serve as a clear guide for future quantum simulation experiments of $2+1$D LGTs.