Entanglement negativity via the replica trick: A quantum Monte Carlo approach
Entanglement negativity via the replica trick: A quantum Monte Carlo approach
复制标题
通过复制技巧的纠缠负性：量子蒙特卡罗方法
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
A. Lauchli
中科院分区：
文献类型：
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作者：
Chia;V. Alba;L. Bonnes;Pochung Chen;A. Lauchli
受共形场论（CFT）最新发展的启发，我们设计了一种量子蒙特卡罗（QMC）方法来计算有限温度下部分转置约化密度矩阵的矩。这些被用来构建与负性相关的尺度不变组合，负性是嵌入在链中的两个区间的纠缠的真实度量。这些量可以作为临界性的见证。特别是，我们研究了一维硬核玻色子模型的矩的尺度不变组合。对于两个相邻的时间间隔不寻常的有限大小的更正，显示奇偶校验的影响，振荡与填充依赖期。在有边界的情况下，这些问题更加突出。对于大型连锁店，我们发现与CFT完全一致。相反，对于不相交的区间，校正更严重，并且CFT仅渐进地恢复。此外，我们提供的证据表明，他们的指数是相同的管理互信息的更正。此外，我们还研究了超流相中的一维Bose-Hubbard模型。值得注意的是，有限尺寸效应较小，QMC数据已经与中等大尺寸的CFT令人印象深刻的一致。
Motivated by recent developments in conformal field theory (CFT), we devise a Quantum Monte Carlo (QMC) method to calculate the moments of the partially transposed reduced density matrix at finite temperature. These are used to construct scale invariant combinations that are related to the negativity, a true measure of entanglement for two intervals embedded in a chain. These quantities can serve as witnesses of criticality. In particular, we study several scale invariant combinations of the moments for the 1D hard-core boson model. For two adjacent intervals unusual finite size corrections are present, showing parity effects that oscillate with a filling dependent period. These are more pronounced in the presence of boundaries. For large chains we find perfect agreement with CFT. Oppositely, for disjoint intervals corrections are more severe and CFT is recovered only asymptotically. Furthermore, we provide evidence that their exponent is the same as that governing the corrections of the mutual information. Additionally we study the 1D Bose-Hubbard model in the superfluid phase. Remarkably, the finite-size effects are smaller and QMC data are already in impressive agreement with CFT at moderate large sizes.