标题： $XY$模型中纠缠重正规化的空间依赖性 显示英文标题

标题： Spatial dependence of entanglement renormalization in $XY$ model

摘要： 本文通过实施量子重整化群（QRG）技术，对一维、二维和三维空间中纠缠重整化的比较研究及其与临界点附近量子相变（QPT）的关系进行了探讨。采用卡丹诺夫块状方法，在所有空间维度下获得了自旋-1/2$XY$模型的保真度。结果显示，随着从低维到高维空间的移动，其定性行为相似，但在热力学极限下实现量子相变所需的迭代次数减少。我们发现，对于二维和三维自旋-1/2$XY$模型，保真度的最大值相对于一维情况的最大值减少了$1/n$ $(n=2,3)$ 倍。此外，我们还研究了标度行为和纠缠指数。我们将一维、二维和三维情况下的结果进行比较，并展示了系统在临界点附近的演化过程。 显示英文摘要

摘要： In this article a comparative study of the renormalization of entanglement in one, two and three dimensional space and its relation with quantum phase transition (QPT) near the critical point is presented by implementing the Quantum Renormalization Group (QRG) technique. Adopting the Kadanoff's block approach, numerical results for the concurrence are obtained for the spin -1/2 $XY$ model in all the spatial dimensions. The results show similar qualitative behavior as we move from the lower to the higher dimensions in space but the number of iterations reduces for achieving the QPT in the thermodynamic limit. We find that in the two dimensional and three dimensional spin -1/2 $XY$ model, maximum values of the concurrence reduce by the factor of $1/n$ $(n=2,3)$ with reference to the maximum value of one dimensional case. Moreover, we study the scaling behavior and the entanglement exponent. We compare the results for one, two and three dimensional cases and illustrate how the system evolves near the critical point.