论文标题
部分可观测时空混沌系统的无模型预测
Augmenting Density Matrix Renormalization Group with Disentanglers
论文作者
论文摘要
密度矩阵重归其化基团（DMRG）及其以基质产物状态（MP）形式的扩展是在过去三十年中研究一维量子系统的选择。但是，由于在波功能ANSATZ中编码的纠缠有限，以维持DMRG的准确性，而在研究二维系统的研究中，系统大小的增加，需要增加资源，这限制了DMRG仅适用于狭窄系统的适用性。在这项工作中，我们介绍了一个新的ANSATZ，其中DMRG与DISENTANGLER进行了增强，以编码区域律般的纠缠熵（在新的Ansatz Scale中支持的纠缠熵为$ L $ for A $ L \ times L $ System）。在新方法中，保留了$ O（d^3）$低计算成本（以$ O（d^4）$和$ d $的开销为$ O（d^4）和$ d $的自由度的维度）。我们在二维横向Ising和Heisenberg模型上使用这种方法执行基准计算。这种新的Ansatz在研究二维量子系统中扩展了DMRG的功能。
Density Matrix Renormalization Group (DMRG) and its extensions in the form of Matrix Product States (MPS) are arguably the choice for the study of one dimensional quantum systems in the last three decades. However, due to the limited entanglement encoded in the wave-function ansatz, to maintain the accuracy of DMRG with the increase of the system size in the study of two dimensional systems, exponentially increased resources are required, which limits the applicability of DMRG to only narrow systems. In this work, we introduce a new ansatz in which DMRG is augmented with disentanglers to encode area-law-like entanglement entropy (entanglement entropy supported in the new ansatz scales as $l$ for a $l \times l$ system). In the new method, the $O(D^3)$ low computational cost of DMRG is kept (with an overhead of $O(d^4)$ and $d$ the dimension of the physical degree of freedom). We perform benchmark calculations with this approach on the two dimensional transverse Ising and Heisenberg models. This new ansatz extends the power of DMRG in the study of two-dimensional quantum systems.
