标题： 有限温度下三角晶格量子环模型中的相变及分数量化的残留现象 显示英文标题

标题： Phase transitions and remnants of fractionalization at finite temperature in the triangular lattice quantum loop model

摘要： 量子环和二聚物模型是具有局部约束的典型关联系统。 在统计力学中有着自然的基础，它们与各种重要的物理概念和系统直接相关，如拓扑序、格点规范理论、几何阻挫，或最近的里德伯阵列量子模拟器。 然而，在非双分几何的重要类别中，热涨落如何与约束相互作用尚未被探索。 在这里，我们通过无偏量子蒙特卡洛模拟和场论分析，研究了三角晶格上量子环模型的有限温度相图。 我们发现最近识别的“隐藏”子涡旋晶格（VP）量子晶体~\cite{ran2024hidden}经历了一个有限温度的连续相变，该相变平滑地连接到分隔 VP 和$\mathbb{Z}_{2}$量子自旋液体相的 (2+1)d 立方*量子临界点。 这个有限温度相变具有{\it 热学分数化}的独特性质，即立方序参量——晶格环共振——及其组成部分——子涡旋场——都表现出独立的临界性特征。 这一相变与晶格向列相和高温无序相之间的三态 Potts 相变相连。 我们讨论了这些结果对当前量子模拟平台实验的相关性。 显示英文摘要

摘要： The quantum loop and dimer models are archetypal correlated systems with local constraints. With natural foundations in statistical mechanics, they are of direct relevance to various important physical concepts and systems, such as topological order, lattice gauge theories, geometric frustrations, or more recently Rydberg arrays quantum simulators. However, how the thermal fluctuations interact with constraints has not been explored in the important class of non-bipartite geometries. Here we study, via unbiased quantum Monte Carlo simulations and field theoretical analysis, the finite-temperature phase diagram of the quantum loop model on the triangular lattice. We discover that the recently identified, "hidden" vison plaquette (VP) quantum crystal~\cite{ran2024hidden} experiences a finite-temperature continuous transition, which smoothly connects to the (2+1)d Cubic* quantum critical point separating the VP and $\mathbb{Z}_{2}$ quantum spin liquid phases. This finite-temperature phase transition acquires a unique property of {\it thermal fractionalization}, in that, both the cubic order parameter -- the plaquette loop resonance -- and its constituent -- the vison field -- exhibit independent criticality signatures. This phase transition is connected to a 3-state Potts transition between the lattice nematic phase and the high-temperature disordered phase. We discuss the relevance of our results for current experiments on quantum simulation platforms.