论文标题
张量网状状态和格林的功能蒙特卡洛的组合
Combination of Tensor Network States and Green's function Monte Carlo
论文作者
论文摘要
我们提出了一种研究量子多体系统的基础状态的方法，其中张量化网络状态（TNS）（特殊预测的纠缠对状态（PEPS））和格林的功能蒙特卡洛（GFMC）合并了。通过设计，PEP编码的区域定律，该法律控制着具有短距离相互作用的量子系统中纠缠熵的缩放，但受键尺寸（D）的高计算复杂性缩放的阻碍。 GFMC是一种高效的方法，但通常遭受臭名昭著的负符号问题，可以通过固定节点近似来避免，其中使用指导波函数来修改采样过程。缺乏负标志问题的权衡是通过指导波函数引入系统错误。在这项工作中，我们结合了这两种PEPS和GFMC，以利用它们两个。 PEP是非常准确的变分波函数，而同时，GFMC中只需要单层张量网络的收缩，这大大降低了成本。此外，保证在GFMC中获得的能量是变异性的，并且低于引导PEPS波函数的变异能量。提供了$ J_1 $ - $ J_2 $ HEISENBERG模型的基准结果。
We propose an approach to study the ground state of quantum many-body systems in which Tensor Network States (TNS), specifically Projected Entangled Pair States (PEPS), and Green's function Monte Carlo (GFMC) are combined. PEPS, by design, encode the area law which governs the scaling of entanglement entropy in quantum systems with short range interactions but are hindered by the high computational complexity scaling with bond dimension (D). GFMC is a highly efficient method, but it usually suffers from the infamous negative sign problem which can be avoided by the fixed node approximation in which a guiding wave function is utilized to modify the sampling process. The trade-off for the absence of negative sign problem is the introduction of systematic error by guiding wave function. In this work, we combine these two methods, PEPS and GFMC, to take advantage of both of them. PEPS are very accurate variational wave functions, while at the same time, only contractions of single-layer tensor network are necessary in GFMC, which reduces the cost substantially. Moreover, energy obtained in GFMC is guaranteed to be variational and lower than the variational energy of the guiding PEPS wave function. Benchmark results of $J_1$-$J_2$ Heisenberg model on square lattice are provided.
