Quantum impurity entanglement
Quantum impurity entanglement
复制标题
量子杂质纠缠
DOI：
--
复制
发表时间：
2007
期刊：
影响因子：
--
通讯作者：
I. Affleck
中科院分区：
文献类型：
--
作者：
Erik S. Sørensen;M. Chang;N. Laflorencie;I. Affleck
用解析方法和大规模数值密度矩阵重整化群方法研究了含杂质的J1-J2，S = 1/2量子自旋链中的纠缠.纠缠是根据冯诺依曼熵S = −TrρAlogρA来研究的，对于链的大小为r的子系统A。定义了杂质对纠缠熵均匀部分Simp的贡献，并详细分析了模型的无隙态J2≤ J2 c和二聚态J2> J2 c。该量子杂质模型属于单通道近藤模型的普适性类，并且表明，以一种相当普遍的方式，无间隙相中杂质的存在，J2≤ J2 c，会产生大的长度尺度ξK，与杂质的屏蔽有关，近藤屏蔽云的尺寸。近藤物理学的普适性意味着大小为R的系统的标度形式为Simp（r/K，r/R）。数值结果清楚地表明这种缩放。在临界点处，J2 c，一种基于费米液体图像的分析方法，在距离和能量标度下都是有效的，并且在T = 0处得到了分析结果，表明对于有限R，Simp = π <$K[1+π（1−r/R）cot（πr/R）]/（12 R）。当T>0时，在热力学极限下，我们得到Simp = [π2 <$KT/（6v）]coth（2πrT/v），其中v为自旋波速度。在二聚化阶段，我们提出了一个吸引人的纠缠图，它是由一个薄的孤子（TS）和杂质价键（IVB）和单粒子纠缠（SPE）的概念来描述的。的TS-分析允许变分计算的二聚相的完全纠缠，似乎是准确的热力学极限在Majumdar-Ghosh点，J2 = J1/2，和令人惊讶的精确，甚至接近临界点J2 c。在附录中，我们进一步利用TS-算符计算了Majumdar-Ghosh点处的纠缠熵，并讨论了有限温度纠缠熵S（T）与热熵Sth（T）之间的关系。最后讨论了Simp的交替部分及其与边界诱导二聚化的关系。
Entanglement in J1–J2, S = 1/2 quantum spin chains with an impurity is studied using analytic methods as well as large scale numerical density matrix renormalization group methods. The entanglement is investigated in terms of the von Neumann entropy, S = −TrρAlogρA, for a subsystem A of size r of the chain. The impurity contribution to the uniform part of the entanglement entropy, Simp, is defined and analysed in detail in both the gapless, J2≤J2c, as well as the dimerized phase, J2>J2c, of the model. This quantum impurity model is in the universality class of the single channel Kondo model and it is shown that in a quite universal way the presence of the impurity in the gapless phase, J2≤J2c, gives rise to a large length scale, ξK, associated with the screening of the impurity, the size of the Kondo screening cloud. The universality of Kondo physics then implies scaling of the form Simp(r/ξK,r/R) for a system of size R. Numerical results are presented clearly demonstrating this scaling. At the critical point, J2c, an analytic approach based on a Fermi liquid picture, valid at distances and energy scales , is developed and analytic results at T = 0 are obtained showing Simp = πξK[1+π(1−r/R)cot(πr/R)]/(12R) for finite R. For T>0, in the thermodynamic limit, we find Simp = [π2ξKT/(6v)]coth(2πrT/v), with v the spin-wave velocity. In the dimerized phase an appealing picture of the entanglement is developed in terms of a thin soliton (TS) ansatz and the notions of impurity valence bonds (IVB) and single particle entanglement (SPE) are introduced. The TS-ansatz permits a variational calculation of the complete entanglement in the dimerized phase that appears to be exact in the thermodynamic limit at the Majumdar–Ghosh point, J2 = J1/2, and surprisingly precise even close to the critical point J2c. In the appendices the TS-ansatz is further used to calculate and with high precision at the Majumdar–Ghosh point and the relation between the finite temperature entanglement entropy, S(T), and the thermal entropy, Sth(T), is discussed. Finally, the alternating part of Simp is discussed, together with its relation to the boundary induced dimerization.