用虚拟里斯翁模拟格点规范理论
Simulating Lattice Gauge Theories with Virtual Rishons
AI总结：
本文提出了一种基于虚拟里斯翁的框架，用于模拟格点规范理论，通过量子比特编码规范和物质自由度，并在U(1)规范理论中验证了其在不同维度下的有效性。
摘要：
经典张量网络和混合量子-经典算法是研究格点规范理论实时性质的有希望候选者。本文开发了一个新的框架，通过在中间步骤应用量子链接虚拟里斯翁表示来强制规范对称性。关键的是，规范和物质自由度作为动态变量编码为量子比特，使能够分析$d+1$维时空中的规范理论。我们在U(1)规范理论中验证了该框架，包括有和无物质场的情况。对于$d=1$，分析了具有1≤N_f≤3种味的多味辛格模型，在任意边界条件和非零拓扑角下，捕捉到底层威斯-祖莫-温特共形场论的特征。对于$d=2$，我们提取了束缚弦张力，与连续极限期望值一致。这些结果确立了虚拟里斯翁框架作为使用经典张量网络和近期量子硬件模拟格点规范理论的可扩展且稳健的方法。
英文摘要：
Classical tensor network and hybrid quantum-classical algorithms are promising candidates for the investigation of real-time properties of lattice gauge theories. We develop here a novel framework which enforces gauge symmetry via a quantum-link virtual rishon representation applied at intermediate steps. Crucially, the gauge and matter degrees of freedom are dynamical variables encoded in terms of qubits, enabling analysis of gauge theories in $d+1$ spacetime dimensions. We benchmark this framework in a U(1) gauge theory with and without matter fields. For $d = 1$, the multi-flavor Schwinger model with $1\leq N_f\leq3$ flavors is analyzed for arbitrary boundary conditions and nonzero topological angle, capturing signatures of the underlying Wess-Zumino-Witten conformal field theory. For $d = 2$, we extract the confining string tension in close agreement with continuum expectations. These results establish the virtual rishon framework as a scalable and robust approach for the simulation of lattice gauge theories using both classical tensor networks as well as near-term quantum hardware.
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