对称热张量网络的完美Born采样用于量子晶格模型

中文摘要 AI 辅助

低温下量子晶格模型的精确计算构成了多体物理中的一项重大挑战。张量网络态的随机采样为攻克这一问题提供了一条有前景的途径；然而，现有方案长期以来面临一个根本性困境——采样效率与对称性加速无法同时实现。在此，我们提出一种针对热张量网络的完美Born采样方法，该方法通过Born规则直接从纯化密度矩阵中进行重要性采样，并通过采样对称性量子数来纳入阿贝尔和非阿贝尔对称性。我们将该方法实现为随机矩阵乘积态（stoMPS）和随机投影纠缠对态（stoPEPS）两种形式，并在大规模量子晶格模型上进行了基准测试。利用stoMPS，我们精确模拟了宽度达$W=10$的圆柱体上的方格哈伯德模型，并将三角晶格哈伯德模型研究至$T/t = 1/64$，揭示了半填充时的标量手性序以及电子掺杂时的动力学铁磁性。我们进一步将stoMPS方法扩展至计算有限温度量子动力学，如哈伯德模型的光学电导率所示，并将其推广至stoPEPS，在$20\ imes20$方格量子伊辛模型量子临界点处进行了展示。我们的方法将高采样效率与完整对称性加速相结合，可作为研究超低温下平衡和动力学性质的最先进框架。

英文摘要

Accurate calculations of quantum lattice models at low temperatures constitute a major challenge in many-body physics. Stochastic sampling of tensor-network states offers a promising route to tackle this problem; however, existing schemes have long faced a fundamental dilemma---sampling efficiency and symmetry acceleration \textit{cannot} be achieved simultaneously. Here we propose a perfect Born sampling approach for thermal tensor networks, which performs importance sampling directly from the purified density matrix via the Born rule and incorporates Abelian and non-Abelian symmetries by sampling symmetry quantum numbers. We benchmark the method, realized as both stochastic matrix product states (stoMPS) and stochastic projected entangled pair states (stoPEPS), on large-scale quantum lattice models. Using stoMPS, we accurately simulate the square-lattice Hubbard model on cylinders up to width $W=10$, and study the triangular-lattice Hubbard model down to $T/t = 1/64$, revealing scalar chiral order at half filling and kinetic ferromagnetism upon electron doping. We further extend the stoMPS method to compute finite-temperature quantum dynamics, as demonstrated by the optical conductivity of the Hubbard model, and generalize it to stoPEPS, as showcased on the $20\times20$ square-lattice quantum Ising model at its quantum critical point. Our method combines high sampling efficiency with full symmetry acceleration, and can be used as a state-of-the-art framework for studying both equilibrium and dynamical properties down to ultralow temperatures.

发表机构

• Peng Huanwu Collaborative Center for Research and Education, Beihang University（彭恒武教育与科研中心，北京航空航天大学）
• Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）
• School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）
• Institute of Fundamental Physics and Quantum Technology, Ningbo University（宁波大学基础物理与量子技术学院）

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