Data for "Efficient optimization and conceptual barriers in variational finite Projected Entangled-Pair States"

Projected entangled pair states (PEPS) on finite two-dimensional lattices are a natural ansatz for representing ground states of local many-body Hamiltonians, as they inherently satisfy the boundary law of entanglement entropy. In this paper, we propose the optimization of PEPS via an improved formulation of the time-dependent variational principle (TDVP), namely the minimum-step stochastic-reconfguration scheme recently introduced for neural quantum states. We further discuss possible numerical issues that might arise in such a sampling-based approach. In this context, investigate the entanglement properties of random PEPS and find an entanglement phase transition. We note that on one side of this transition, we can identify positive random tensors as product states. To demonstrate the power of the framework described in this paper, we apply the PEPS to study the notoriously challenging chiral spin liquids. Moreover, we exhibit our approach's capability to naturally handle long-range interactions by exploring the phase diagram of Rydberg atom arrays with long-range interactions. We further provide parallelized easy-to-use code, allowing the straightforward application of our method to general Hamiltonians composed of local interaction terms. Technical info In the files you will find the resulting data needed to reproduce the plots for the paper Efficient optimization and conceptual barriers in variational finite Projected Entangled-Pair States. Note that the simulation data is in the JLD2 format, which can be read either directly in Julia or by any hdf5-compatible library. Note that the fPEPS code to reproduce these results will be provided on Github after publication, and is available upon request before that. The other part of the library where sampling tdvp has been implemented can be found under QuantumNaturalGradient.jl投影纠缠对态（Projected Entangled Pair States，PEPS）是定义于有限二维晶格上的自然试探波函数，用于表征局域多体哈密顿量的基态——因其天然满足纠缠熵边界定律。本文中，我们提出基于改进型含时变分原理（Time-Dependent Variational Principle，TDVP）的PEPS优化方案，即针对神经量子态新近提出的最小步长随机重配置策略。我们进一步讨论了此类基于采样的方法可能出现的数值问题。在此框架下，我们研究了随机PEPS的纠缠特性，并发现了一类纠缠相变。我们注意到，在该相变的一侧，可将正随机张量识别为直积态。 为验证本文所提框架的有效性，我们将PEPS应用于极具挑战性的手性自旋液体研究。此外，我们通过探究具有长程相互作用的里德伯原子阵列的相图，展示了本方法可自然处理长程相互作用的能力。我们还提供了并行化且易于使用的代码，可将本方法直接应用于由局域相互作用项构成的一般哈密顿量。 技术说明 本数据集文件包含复现论文《变分有限投影纠缠对态的高效优化与概念壁垒》（Efficient optimization and conceptual barriers in variational finite Projected Entangled-Pair States）所需的全部绘图数据。请注意，仿真数据采用JLD2格式，可直接在Julia语言环境中读取，或通过任意兼容HDF5的库进行读取。请注意，复现本研究结果所需的fPEPS代码将在论文发表后上传至GitHub，发表前可通过申请获取。本库中实现了采样型TDVP的另一部分代码，可在QuantumNaturalGradient.jl中获取。