Entanglement entropy of two disjoint intervals separated by one spin in a chain of free fermion*
Entanglement entropy of two disjoint intervals separated by one spin in a chain of free fermion*
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自由费米子链中由一个自旋分隔的两个不相交区间的纠缠熵*
DOI：
10.1088/1751-8121/ab9cf2
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
Virtanen, J. A.
中科院分区：
文献类型：
--
作者：
Brightmore, L.;Gehér, G. P.;Its, A. R.;Korepin, V. E.;Mezzadri, F.;Mo, M. Y.;Virtanen, J. A.
我们计算自由费米子链的非连续子系统的纠缠熵。起点是 Jin 和 Korepin 建议的公式，arXiv: 1104.1004，用于计算具有晶格位点 P={1, 2,..., m}∪{2m+ 1, 2m+ 2,..., 3m} 的两个不相交区间的约化态密度，该公式适用于该模型。作为该系统渐近分析的第一步，我们将其简化为仅由一个站点分隔的两个不相交区间，并且我们严格计算这两个块与链的其余部分之间的互信息。为了计算熵，我们需要使用 Riemann-Hilbert 方法研究具有 Fisher-Hartwig 符号的逆 Toeplitz 矩阵的渐近行为。
We calculate the entanglement entropy of a non-contiguous subsystem of a chain of free fermions. The starting point is a formula suggested by Jin and Korepin, arXiv: 1104.1004, for the reduced density of states of two disjoint intervals with lattice sites P={1, 2,..., m}∪{2m+ 1, 2m+ 2,..., 3m}, which applies to this model. As a first step in the asymptotic analysis of this system, we consider its simplification to two disjoint intervals separated just by one site, and we rigorously calculate the mutual information between these two blocks and the rest of the chain. In order to compute the entropy we need to study the asymptotic behaviour of an inverse Toeplitz matrix with Fisher–Hartwig symbol using the the Riemann–Hilbert method.