在Z₂晶格规范理论中引入物质诱导的plaquette项
Matter-induced plaquette terms in a $\mathbb{Z}_2$ lattice gauge theory
AI总结：
本研究展示了动态U(1)物质如何诱导复杂多体相互作用，从而自然产生强plaquette项，为实现拓扑量子自旋液体提供新途径。
摘要：
晶格规范理论（LGTs）提供了一个强大的框架，用于研究束缚、拓扑序和奇异量子物质。特别是，束缚现象——动态物质与规范场耦合并形成束缚态——仍然是一个开放性问题。此外，LGTs可以提供量子自旋液体的低能描述，这是当前实验研究的重点。然而，LGTs的研究通常受到理论上的限制，因为它们的数值复杂性很高，实验上在实现具有挑战性的多体相互作用（如plaquette项，这对于实现许多奇异物质相至关重要）时也面临困难。本文研究了一个（2+1）维Z₂LGT，其与具有全局U(1)对称性的硬核心玻色子物质耦合，并展示了动态物质自然诱导出显著的plaquette相互作用，即使在哈密顿量中没有显式的plaquette项。通过结合密度矩阵重整化群模拟和神经量子态计算，直到20×20的系统规模，我们分析了该模型在不同填充和电场强度下的表现。在小耦合强度下，我们发现对于广泛的填充范围，plaquette期望值很大，与系统大小无关，但在更强的电场下会减小。此外，我们观察到在弱耦合强度下存在束缚-解束缚相变的迹象。我们的结果表明，动态的U(1)物质可以诱导复杂的多体相互作用，这表明了一条自然实现强plaquette项的道路，并为实现由大能隙保护的拓扑量子自旋液体铺平了道路。
英文摘要：
Lattice gauge theories (LGTs) provide a powerful framework for studying confinement, topological order, and exotic quantum matter. In particular, the paradigmatic phenomenon of confinement, where dynamical matter is coupled to gauge fields and forms bound states, remains an open problem. In addition, LGTs can provide low-energy descriptions of quantum spin liquids, which is the focus of ongoing experimental research. However, the study of LGTs is often limited theoretically by their numerical complexity and experimentally in implementing challenging multi-body interactions, such as the plaquette terms crucial for the realization of many exotic phases of matter. Here we investigate a $(2+1)$D $\mathbb{Z}_2$ LGT coupled to hard-core bosonic matter featuring a global U(1) symmetry, and show that dynamical matter naturally induces sizable plaquette interactions even in the absence of explicit plaquette terms in the Hamiltonian. Using a combination of density matrix renormalization group simulations and neural quantum state calculations up to a system size of $20 \times 20$, we analyze the model across different fillings and electric field strengths. At small coupling strength, we find a large plaquette expectation value, independent of system size, for a wide range of fillings, which decreases in the presence of stronger electric fields. Furthermore, we observe signatures of a confinement-deconfinement transition at weak coupling strengths. Our results demonstrate that dynamical U(1) matter can induce complex multi-body interactions, suggesting a natural route to the realization of strong plaquette terms and paving the way for realizing a topological quantum spin liquid protected by a large gap.
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