论文标题
具有非平凡单位细胞的二维张量网络的有效变分收缩
Efficient variational contraction of two-dimensional tensor networks with a non-trivial unit cell
论文作者
论文摘要
张量网络提供了一种有效类别的状态，这些状态忠实地捕获经典统计力学中强烈相关的量子模型和系统。虽然现在可以将张量网络视为在这种复杂多体系统的描述中成为标准工具，但基于此类状态的最佳变异原理几乎不太明显。在这项工作中，我们概括了最近提出的一个变异均匀基质产物算法，用于在热力学极限中捕获一维量子晶格，以研究具有非平常单位细胞的常规二维张量网络。该算法的关键属性是计算工作，它在单位单元格的大小上呈线性缩放而不是指数缩放。我们证明了我们的方法在计算平方晶格上的反铁磁性ISING模型和相互作用二聚体的经典分区功能以及量子掺杂的谐振价键状态的表现。
Tensor network states provide an efficient class of states that faithfully capture strongly correlated quantum models and systems in classical statistical mechanics. While tensor networks can now be seen as becoming standard tools in the description of such complex many-body systems, close to optimal variational principles based on such states are less obvious to come by. In this work, we generalize a recently proposed variational uniform matrix product state algorithm for capturing one-dimensional quantum lattices in the thermodynamic limit, to the study of regular two-dimensional tensor networks with a non-trivial unit cell. A key property of the algorithm is a computational effort that scales linearly rather than exponentially in the size of the unit cell. We demonstrate the performance of our approach on the computation of the classical partition functions of the antiferromagnetic Ising model and interacting dimers on the square lattice, as well as of a quantum doped resonating valence bond state.
