Numerical calculations on the relative entanglement entropy in critical spin chains
Numerical calculations on the relative entanglement entropy in critical spin chains
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DOI：
10.1088/1742-5468/aa85c1
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发表时间：
2017-05
期刊：
影响因子：
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通讯作者：
Yuya O. Nakagawa;Tomonori Ugajin
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文献类型：
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作者：
Yuya O. Nakagawa;Tomonori Ugajin
研究了临界自旋链S=1/2XXZ链和临界态横场Ising链中各初级激发态间的相对纠缠熵。对于S=1/2XXZ链，对应于c=1自由玻色子共形场论（CFT），我们用精确对角化方法数值计算了相对EE，发现与CFT的预言完全一致.对于临界态的横向场Ising链，对应于c=1/2的Ising CFT，我们解析地把它的相对EE与S=1/2的XXZ链的EE联系起来，并用数值方法证实了这种关系。我们还计算了“三明治”Rényi相对EE和再次的数值结果与分析预测吻合得很好。我们的结果是第一次直接确认的临界自旋链中的初级激发态的相对EE的CFT预测。
We study the relative entanglement entropy (EE) among various primary excited states in two critical spin chains: the S=1/2 XXZ chain and the transverse field Ising chain at criticality. For the S=1/2 XXZ chain, which corresponds to c=1 free boson conformal field theory (CFT), we numerically calculate the relative EE by exact diagonalization and find a perfect agreement with the predictions by the CFT. For the transverse field Ising chain at criticality, which corresponds to the c=1/2 Ising CFT, we analytically relate its relative EE to that of the S=1/2 XXZ chain and confirm the relation numerically. We also calculate the ‘sandwiched’ Rényi relative EE and again the numerical results agree well with the analytical predictions. Our results are the first direct confirmation of the CFT predictions on the relative EE of the primary excited states in critical spin chains.