零空间引导的量子多体系统自适应自举方法

中文摘要 AI 辅助

我们提出了一种零空间引导的自适应（NGA）自举方法，通过动态且增量地优化自举基，提高了量子多体基态能量的下界。在每次迭代中，优化后的矩矩阵揭示出一个由饱和正定方向组成的零空间，该零空间可直观地解释为近似基态子空间的湮灭算符。NGA自举随后修剪具有较小零空间杠杆的算符，并沿这些零方向的后代扩展基。通过将NGA自举应用于横场伊辛链，我们获得了近乎精确的能量下界，因为该算法自动从最小局部自举基中发现了以约旦-维格纳费米子表示的本征算符结构。对于哈伯德链，它比现有最优的能量下界提高了最多两个数量级，在强关联区域中误差范围从$10^{-3}$降至$10^{-5}$。我们进一步展示了NGA框架可用于改进一般可观测量的认证双侧界。此外，自举误差随计算资源的增加近似呈幂律下降。这些结果表明，我们的方法为一般量子多体系统的精确自举提供了一条实用且可扩展的途径。

英文摘要

We introduce a nullspace-guided adaptive (NGA) bootstrap method that improves the energy lower bounds of quantum many-body ground states by refining the bootstrap basis in a dynamic and incremental way. At each iteration, the optimized moment matrix reveals a nullspace of saturated positivity directions, which is intuitively interpreted as annihilators of the approximate ground-state subspace. The NGA bootstrap then prunes operators with small nullspace leverage and grows the basis along descendants of these null directions. By applying the NGA bootstrap to the transverse-field Ising chain, we obtain nearly exact energy lower bounds because the algorithm automatically discovers the eigenoperator structure in terms of Jordan-Wigner fermions from a minimal local bootstrap basis. For the Hubbard chain, it improves upon state-of-the-art energy lower bounds by up to two orders of magnitude, reaching errors ranging from $10^{-3}$ down to $10^{-5}$ in the strongly correlated regimes. We further show that the NGA framework can be used to improve the certified two-sided bounds on general observables. In addition, the bootstrap error decreases approximately as a power law with increasing computational resources. These results suggest that our method provides a practical and scalable route toward accurate bootstrap of general quantum many-body systems.

发表机构

• State Key Laboratory of Surface Physics, Fudan University（复旦大学表面物理国家重点实验室）
• Center for Field Theory and Particle Physics, Department of Physics, Fudan University（复旦大学物理学院场论与粒子物理中心）
• Collaborative Innovation Center of Advanced Microstructures（先进微结构协同创新中心）
• Hefei National Laboratory（合肥国家实验室）

机构由 AI 辅助整理，请以论文原文为准。

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13 pages, 5 figures