具有远程反铁磁相互作用的无序量子自旋链的纠缠特性

Y. Mohdeb, J. Vahedi, N. Moure, A. Roshani, Hyunyong Lee, R. Bhatt, S. Kettemann, S. Haas
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引用次数: 3

摘要

我们研究了具有随机远程耦合的量子自旋链中的并发熵和纠缠熵,它们在空间上以幂律指数$\alpha$衰减。利用强无序重整化群(SDRG)技术,通过对主方程的解析解,我们发现了一个强无序不动点,其特征是耦合的不动点分布具有有限动力指数,该不动点一致地描述了系统在$\alpha > 1/2$区域内的状态。SDRG方法的数值实现产生了平均并发的幂律空间衰减,这也被精确的数值对角化所证实。然而,我们发现最低阶SDRG方法不足以获得并发的典型值。因此,我们实现了一种校正方案,使我们能够获得随机单重态的阶校正。这种方法产生并发的典型值的幂律空间衰减,我们通过修正的数值实现和分析得出。接下来,使用数值SDRG,发现所有$\alpha$的纠缠熵(EE)呈对数增强,对应于有效中心电荷$c = {\rm ln} 2$的临界行为,与$\alpha$无关。这是由解析推导证实的。利用数值精确对角化(ED),我们证实了EE的对数增强和对$\alpha$的弱依赖。对于大范围的距离$l$, EE符合中心电荷接近$c=1$的临界行为,这与具有幂- α衰变相互作用$\ α =2$的干净Haldane-Shastry模型相同。与这一观察结果一致,我们发现使用ED,并发表现出幂律衰减,尽管幂指数比SDRG得到的要小。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Entanglement properties of disordered quantum spin chains with long-range antiferromagnetic interactions
We examine the concurrence and entanglement entropy in quantum spin chains with random long-range couplings, spatially decaying with a power-law exponent $\alpha$. Using the strong disorder renormalization group (SDRG) technique, we find by analytical solution of the master equation a strong disorder fixed point, characterized by a fixed point distribution of the couplings with a finite dynamical exponent, which describes the system consistently in the regime $\alpha > 1/2$. A numerical implementation of the SDRG method yields a power law spatial decay of the average concurrence, which is also confirmed by exact numerical diagonalization. However, we find that the lowest-order SDRG approach is not sufficient to obtain the typical value of the concurrence. We therefore implement a correction scheme which allows us to obtain the leading order corrections to the random singlet state. This approach yields a power-law spatial decay of the typical value of the concurrence, which we derive both by a numerical implementation of the corrections and by analytics. Next, using numerical SDRG, the entanglement entropy (EE) is found to be logarithmically enhanced for all $\alpha$, corresponding to a critical behavior with an effective central charge $c = {\rm ln} 2$, independent of $\alpha$. This is confirmed by an analytical derivation. Using numerical exact diagonalization (ED), we confirm the logarithmic enhancement of the EE and a weak dependence on $\alpha$. For a wide range of distances $l$, the EE fits a critical behavior with a central charge close to $c=1$, which is the same as for the clean Haldane-Shastry model with a power-la-decaying interaction with $\alpha =2$. Consistent with this observation, we find using ED that the concurrence shows power law decay, albeit with smaller power exponents than obtained by SDRG.
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