We study the entanglement Hamiltonian for finite intervals in infinite quantum chains for two different free-particle systems: coupled harmonic oscillators and fermionic hopping models with dimerization. Working in the ground state, the entanglement Hamiltonian describes again free bosons or fermions and is obtained from the correlation functions via high-precision numerics for up to several hundred sites. Far away from criticality, the dominant on-site and nearest-neighbour terms have triangular profiles that can be understood from the analytical results for a half-infinite interval. Near criticality, the longer-range couplings, although small, lead to a more complex picture. A comparison between the exact spectra and entanglement entropies and those resulting from the dominant terms in the Hamiltonian is also reported.

中文翻译：

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非临界量子链的纠缠哈密顿量

我们研究了两种不同自由粒子系统的无限量子链中有限区间的纠缠哈密顿量：耦合谐振子和具有二聚化的费米子跳跃模型。在基态下工作，纠缠哈密顿量再次描述自由玻色子或费米子，并通过高达数百个位点的高精度数值从相关函数中获得。远离临界状态，主要的现场和最近邻项具有三角形轮廓，可以从半无限区间的分析结果中理解。接近临界点时，远程耦合虽然很小，但会导致更复杂的情况。还报告了精确光谱和纠缠熵与哈密顿量中的主导项产生的那些之间的比较。