Spindrift：从受限路径积分蒙特卡罗中的热纯度学习量子简并性
Spindrift: Learning quantum degeneracy from thermal purity in restricted path integral Monte Carlo
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中文总结 AI 辅助
Spindrift是一种变分密度矩阵方法，通过受限Worm算法样本的正则化Bloch残差学习多体费米子密度矩阵，在二维简谐势阱模拟中降低了受限热力学能量，为有限温度量子蒙特卡罗提供了自洽学习节点结构的稳定框架。
中文摘要 AI 辅助
受限路径积分蒙特卡罗（RPIMC）通过将路径限制在试探密度矩阵的节点口袋内，规避了费米子符号问题的波动，从而恢复了多项式缩放。然而，该节点表面必须从其他地方提供；除非它是精确的，否则会引入固定节点能量误差。在此，我们介绍\textsc{Spindrift}，一种变分密度矩阵方法，它通过在受限Worm算法抽取的样本上评估正则化Bloch残差，学习多体费米子密度矩阵。受量子力学在高温下“纯度”（其中动能占主导）这一观察的启发，我们沿温度（虚时间）课程训练密度矩阵，学习对初始自由粒子参考的越来越大的修正。我们用置换等变连续归一化流对模型进行参数化，以生成准粒子回流轨迹，该轨迹由对称Jastrow因子调制。该架构在整个训练过程中保证了精确的费米子反对称性和空间对称性。在二维简谐势阱中模拟N=3个相互作用费米子，我们证明了稳定的课程训练。学习到的速度场使节点结构从自由粒子参考平滑变形。Open-Worm G- sector捕获为节点精度提供了自然诊断。尽管当前估计器中缺乏节点作用妨碍了绝对基准测试，但\textsc{Spindrift}在每个温度下都降低了相对于自由粒子参考的受限热力学能量，为有限温度量子蒙特卡罗建立了一个稳定的、物理信息的框架，其中节点结构是自洽学习的。
英文摘要
Restricted path integral Monte Carlo (RPIMC) sidesteps the fluctuating Fermion sign problem by confining paths within nodal regions of a trial density matrix, thereby recovering polynomial scaling. However, this nodal surface must be provided from elsewhere; unless it is exact, it introduces a fixed-node energy error. Here we introduce \textsc{Spindrift}, a Variational Density Matrix approach that learns the many-body Fermionic density matrix from a regularised Bloch residual, evaluated on samples drawn by a restricted Worm algorithm. Motivated by the `purity' of quantum statistical mechanics at high temperature (where kinetic energy dominates), we train the density matrix along an imaginary-time (descending temperature) curriculum from an exact infinite-temperature heat-kernel starting point, learning the condensation of quantum correlations as temperature drops, through successive corrections to the previous reference. We parametrise our model with a permutation-equivariant continuous normalising flow to generate quasi-particle backflow trajectories, modulated by a symmetric Jastrow factor. This architecture guarantees exact Fermionic antisymmetry and spatial symmetry throughout training. Simulating $N=3$ interacting Fermions in a two-dimensional harmonic trap, we demonstrate stable curriculum training. The learnt velocity field smoothly deforms the nodal structure away from the free-particle reference. Open-Worm G-sector trapping provides a natural diagnostic for nodal accuracy. \textsc{Spindrift} systematically lowers the restricted energy relative to the free-particle reference across all temperatures and successfully reproduces the benchmark energy at $β=1$, establishing a stable, physics-informed framework for finite-temperature quantum Monte Carlo where the nodal structure is learnt self-consistently.
