Kibble-Zurek动力学在二维阻挫系统中的神经基态子空间方法

中文摘要 AI 辅助

当一个强相互作用量子多体系统被驱动穿过连续相变时产生的普适标度，为平衡临界性提供了动力学探针。在二维中数值上进入这一区域具有挑战性，因为它需要对相关多体态在多个系统尺寸和驱动速率下进行精确的实时演化。我们引入了一种用于近绝热动力学的神经基态子空间（NFS）方法。一个基础神经网络量子态表示沿驱动路径的基态流形，一个小型保真度选择的子集定义了一个固定的变分子空间。多体薛定谔方程随后简化为少数线性系数的演化，投影算符可在斜坡时间上重复使用。我们在二维横场伊辛模型上验证了该方法，恢复了预期的Kibble-Zurek标度和临界指数，与基态量子蒙特卡洛估计定量一致。应用于阻挫方格$J_1$-$J_2$海森堡模型，最大至$16 \times 16$簇，我们的方法提供了Kibble-Zurek机制在$J_2/J_1=0.49$处Néel到自旋液体转变中的强数值证据，在固定$z=1$时得到${\nu=1.23(15)}$和${\eta=0.409(19)}$，与静态估计一致，并支持所提出的连续临界行为。

英文摘要

Universal scaling generated when a strongly interacting quantum many-body system is driven across a continuous phase transition provides a dynamical probe of equilibrium criticality. Accessing this regime numerically in two dimensions is challenging because it requires accurate real-time evolution of correlated many-body states over many system sizes and driving rates. We introduce a Neural Foundation-state Subspace (NFS) method for near-adiabatic dynamics. A foundation neural-network quantum state represents the ground-state manifold along the driving path, and a small fidelity-selected subset defines a fixed variational subspace. The many-body Schrödinger equation then reduces to the evolution of a few linear coefficients, with projected operators reusable across ramp times. We validate the method on the two-dimensional transverse-field Ising model, recovering the expected Kibble-Zurek scaling and critical exponents in quantitative agreement with ground-state quantum Monte Carlo estimates. Applied to the frustrated square-lattice $J_1$-$J_2$ Heisenberg model up to $16 \times 16$ clusters, our approach provides strong numerical evidence of Kibble-Zurek mechanism across the Néel-to-spin-liquid transition at $J_2/J_1=0.49$, yielding ${ν=1.23(15)}$ and ${η=0.409(19)}$ at fixed $z=1$, consistent with static estimates and supporting the proposed continuous critical behavior.

发表机构

• Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院物理研究所）
• Center for Computational Quantum Physics, Flatiron Institute（平顿研究所计算量子物理中心）

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