Entanglement renormalization in two spatial dimensions.
Entanglement renormalization in two spatial dimensions.
复制标题
二维空间维度的纠缠重整化。
DOI：
10.1103/physrevlett.102.180406
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发表时间：
2008
影响因子：
8.6
通讯作者：
G. Vidal
中科院分区：
文献类型：
--
作者：
G. Evenbly;G. Vidal
我们提出并测试了一种能够解决大型二维量子晶格系统的纠缠重整化方案。在平移不变系统中，模拟成本仅随着晶格尺寸的对数而增长；在量子临界点，模拟成本变得与晶格尺寸无关，并且可以分析无限系统。我们通过研究具有周期性边界条件的线性尺寸 L={6, 9, 18, 54, 无穷大} 的方晶格上的二维量子伊辛模型的低能特性来证明该方案的性能。我们计算基态并评估局部可观测量和两点相关器。我们还对临界磁场和临界指数 beta 进行准确的估计。能隙的计算表明，其在临界点处的比例为 1/L。
We propose and test a scheme for entanglement renormalization capable of addressing large two-dimensional quantum lattice systems. In a translationally invariant system, the cost of simulations grows only as the logarithm of the lattice size; at a quantum critical point, the simulation cost becomes independent of the lattice size and infinite systems can be analyzed. We demonstrate the performance of the scheme by investigating the low energy properties of the 2D quantum Ising model on a square lattice of linear size L={6, 9, 18, 54, infinity} with periodic boundary conditions. We compute the ground state and evaluate local observables and two-point correlators. We also produce accurate estimates of the critical magnetic field and critical exponent beta. A calculation of the energy gap shows that it scales as 1/L at the critical point.