Entanglement negativity and conformal field theory: a Monte Carlo study
Entanglement negativity and conformal field theory: a Monte Carlo study
复制标题
纠缠负性和共形场论：蒙特卡罗研究
DOI：
10.1088/1742-5468/2013/05/p05013
复制
发表时间：
2013
期刊：
影响因子：
--
通讯作者：
V. Alba
中科院分区：
文献类型：
--
作者：
V. Alba
研究了部分转置约化密度矩阵ρ AT2？>在临界量子自旋链中。给定子系统A作为两个块的并集，这是ρA相对于两个块之一的自由度的（矩阵）转置。这也是构造对数负性的主要成分。我们提供了一个新的数值格式，有效地计算所有的时刻ρ AT2？>使用经典的蒙特卡罗模拟。特别是，我们研究了几种组合的时刻是规模不变的临界点。它们的行为在临界伊辛链和各向异性海森堡XXZ链中都得到了充分的表征。对于两个相邻的块，我们发现，在这两个模型，完全符合最近的共形场理论（CFT）的计算。对于不相交块，在伊辛链中有限尺寸修正是不可忽略的。我们证明了它们的指数是相同的，这两个块之间的互信息的不寻常的缩放校正。蒙特卡罗数据完全匹配的理论CFT预测只有在无限区间的渐近极限。Opanimous，在海森堡链标度修正较小，已经在有限（适度大）块大小，蒙特卡罗数据与渐近CFT结果非常吻合。
We investigate the behavior of the moments of the partially transposed reduced density matrix ρ A T 2 ?> in critical quantum spin chains. Given subsystem A as the union of two blocks, this is the (matrix) transpose of ρA with respect to the degrees of freedom of one of the two blocks. This is also the main ingredient for constructing the logarithmic negativity. We provide a new numerical scheme for efficiently calculating all the moments of ρ A T 2 ?> using classical Monte Carlo simulations. In particular we study several combinations of the moments which are scale invariant at a critical point. Their behavior is fully characterized in both the critical Ising and the anisotropic Heisenberg XXZ chains. For two adjacent blocks we find, in both models, full agreement with recent conformal field theory (CFT) calculations. For disjoint blocks, in the Ising chain finite size corrections are nonnegligible. We demonstrate that their exponent is the same as that governing the unusual scaling corrections of the mutual information between the two blocks. Monte Carlo data fully match the theoretical CFT prediction only in the asymptotic limit of infinite intervals. Oppositely, in the Heisenberg chain scaling corrections are smaller and, already at finite (moderately large) block sizes, Monte Carlo data are in excellent agreement with the asymptotic CFT result.
影响因子：
2.9
作者：
S. Marcovitch;A. Retzker;M. Plenio;B. Reznik
通讯作者：
S. Marcovitch;A. Retzker;M. Plenio;B. Reznik