具有更高局域占据数和长程相互作用的相互作用 Hofstadter 模型的神经网络量子态
Neural Network Quantum States for the Interacting Hofstadter Model with Higher Local Occupations and Long-Range Interactions
AI总结：
本文利用二维张量化门控循环神经网络量子态研究具有长程相互作用的 Hofstadter 模型，在高达 12×12 格点系统中识别出气泡晶体和 Wigner 晶体等相，证明 NQS 是模拟当前量子多体系统的有效方法。
摘要：
由于其巨大的表示能力，神经网络量子态（NQS）在当前研究中获得了显著关注。在 NQS 领域的最新进展中，已经证明该方法可以与最先进的数值技术相竞争，使 NQS 成为一种极具吸引力的替代方案，特别是对于大型二维量子系统的模拟。在本研究中，我们展示了循环神经网络（RNN）波函数可用于研究与当前量子多体物理研究相关的系统。具体而言，我们采用二维张量化门控 RNN 来探索具有可变局域 Hilbert 空间截断和长程相互作用的玻色 Hofstadter 模型。首先，我们在正方晶格上对 Hofstadter-Bose-Hubbard（HBH）哈密顿量进行了 RNN-NQS 基准测试。我们发现，尽管波函数具有复杂性，该方法仍能高效地识别并表示大多数基态性质。随后，我们将该方法应用于一个对当前方法而言更具挑战性的模型，即具有长程相互作用的 Hofstadter 模型。该模型描述了在合成磁场作用下晶格上的 Rydberg 修饰原子。我们研究了尺寸高达 $12 \ imes 12$ 格点的系统，并通过调节相互作用范围和填充分数 $ν$ 识别出三种不同的区域。除了在短程相互作用下从 HBH 模型已知的相之外，我们还观察到长程相互作用下的气泡晶体和 Wigner 晶体。尤其令人感兴趣的是在晶格上存在气泡晶体相的证据，因为这为实验寻找可能承载非阿贝尔任意子激发的团簇液相提供了一个起点。在我们的工作中，我们表明 NQS 是当前研究主题中的量子系统的一种高效且可靠的模拟方法。
英文摘要：
Due to their immense representative power, neural network quantum states (NQS) have gained significant interest in current research. In recent advances in the field of NQS, it has been demonstrated that this approach can compete with state-of-the-art numerical techniques, making NQS a compelling alternative, in particular for the simulation of large, two-dimensional quantum systems. In this study, we show that recurrent neural network (RNN) wave functions can be employed to study systems relevant to current research in quantum many-body physics. Specifically, we employ a 2D tensorized gated RNN to explore the bosonic Hofstadter model with a variable local Hilbert space cut-off and long-range interactions. At first, we benchmark the RNN-NQS for the Hofstadter-Bose-Hubbard (HBH) Hamiltonian on a square lattice. We find that this method is, despite the complexity of the wave function, capable of efficiently identifying and representing most ground state properties. Afterwards, we apply the method to an even more challenging model for current methods, namely the Hofstadter model with long-range interactions. This model describes Rydberg-dressed atoms on a lattice subject to a synthetic magnetic field. We study systems of size up to $12 \times 12$ sites and identify three different regimes by tuning the interaction range and the filling fraction $ν$. In addition to phases known from the HBH model at short-ranged interaction, we observe bubble crystals and Wigner crystals for long-ranged interactions. Especially interesting is the evidence of a bubble crystal phase on a lattice, as this gives experiments a starting point for the search of clustered liquid phases, possibly hosting non-Abelian anyon excitations. In our work we show that NQS are an efficient and reliable simulation method for quantum systems, which are the subject of current research.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
