Entanglement or modular Hamiltonians play a crucial role in the investigation of correlations in quantum field theories. In particular, in 1+1 space-time dimensions, the spectra of entanglement Hamiltonians of conformal field theories (CFTs) for certain geometries are related to the spectra of the physical Hamiltonians of corresponding boundary CFTs. As a result, conformal invariance allows exact computation of the spectra of the entanglement Hamiltonians for these models. In this work, we perform this computation of the spectrum of the entanglement Hamiltonian for the free compactified boson CFT over a finite spatial interval. We compare the analytical results obtained for the continuum theory with numerical simulations of a lattice-regularized model for the CFT using density matrix renormalization group technique. To that end, we use a lattice regularization provided by superconducting quantum electronic circuits, built out of Josephson junctions and capacitors. Up to non-universal effects arising due to the lattice regularization, the numerical results are compatible with the predictions of the exact computations.

中文翻译：

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1 + 1 维自由紧致玻色子共形场论的纠缠哈密顿量

纠缠或模哈密顿量在量子场论中的相关性研究中起着至关重要的作用。特别是，在 1+1 时空维度上，保形场论 (CFT) 的纠缠哈密顿量对于某些几何形状的光谱与相应边界 CFT 的物理哈密顿量的光谱有关。因此，保形不变性允许精确计算这些模型的纠缠哈密顿量的谱。在这项工作中，我们在有限空间间隔内对自由紧致玻色子 CFT 的纠缠哈密顿量谱进行了这种计算。我们将连续介质理论的分析结果与使用密度矩阵重整化群技术的 CFT 晶格正则化模型的数值模拟进行比较。为此，我们使用由约瑟夫森结和电容器构成的超导量子电子电路提供的晶格正则化。由于晶格正则化引起的非普遍效应，数值结果与精确计算的预测一致。