Recently, entropy corrections on nonorientable manifolds such as the Klein bottle are proposed as a universal characterization of critical systems with an emergent conformal field theory (CFT). We show that entropy correction on the Klein bottle can be interpreted as a boundary effect via transforming the Klein bottle into an orientable manifold with nonlocal boundary interactions. The interpretation reveals the conceptual connection of the Klein bottle entropy with the celebrated Affleck-Ludwig entropy in boundary CFT. We propose a generic scheme to extract these universal boundary entropies from quantum Monte Carlo calculation of partition function ratios in lattice models. Our numerical results on the Affleck-Ludwig entropy and Klein bottle entropy for the $q$-state quantum Potts chains with $q=2,3$ show excellent agreement with the CFT predictions. For the quantum Potts chain with $q=4$, the Klein bottle entropy slightly deviates from the CFT prediction, which is possibly due to marginally irrelevant terms in the low-energy effective theory.

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共形场论中的普遍边界熵：量子蒙特卡洛研究

近年来，提出了对不可定向歧管（例如Klein瓶）的熵校正，以利用紧急共形场理论（CFT）对关键系统进行通用表征。我们表明，通过将Klein瓶转换为具有非局部边界相互作用的可定向流形，可以将Klein瓶上的熵校正解释为边界效应。该解释揭示了边界CFT中Klein瓶熵与著名的Affleck-Ludwig熵的概念联系。我们提出一种通用方案，从晶格模型中分配函数比率的量子蒙特卡罗计算中提取这些通用边界熵。我们对Affleck-Ludwig熵和Klein瓶熵的数值结果$q$状态量子Potts链具有 $q=\mathrm{2个}，3$与CFT的预测非常吻合。对于量子Potts链$q=4$，Klein瓶的熵稍微偏离了CFT预测，这可能是由于低能效理论中的边际无关项所致。