利用（量子化）张量列加速强耦合非平衡稳态杂质求解器
Accelerating a Strong-Coupling Non-Equilibrium Steady-State Impurity Solver using (Quantics) Tensor Trains
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中文总结 AI 辅助
本研究提出四种积分参数化方式，结合量子化张量列与张量交叉插值加速强耦合非平衡稳态杂质求解器，经基准测试与DMFT验证可降低高阶图计算成本，适用于多类量子杂质计算。
中文摘要 AI 辅助
对强耦合展开的高阶图修正的计算主要受限于高维时序积分的评估。本研究提出并对比了积分项的四种不同参数化方式，以通过张量交叉插值获得低秩（量子化）张量列表示。研究重点关注量子化时间差形式，其中所需的推迟卷积直接以量子化张量列形式执行。通过可控高斯基准测试，分析了不同方法的精度、键维度和计算缩放性。随后在自洽平衡与非平衡DMFT计算中验证了最具前景的形式，并展示了强耦合展开中三阶的计算。最后将求解器扩展至具有推迟密度-密度相互作用的杂质模型，并应用于非平衡扩展DMFT中。结果表明，张量交叉插值大幅降低了高阶图的评估成本，为非平衡量子杂质计算提供了可控、可系统改进的框架。
英文摘要
Including higher order diagrammatic corrections to the strong-coupling expansion is mainly limited by the evaluation of high-dimensional, time-ordered integrals. In this work we present and compare four different parametrizations of the integrands in order to obtain a low-rank (quantics) tensor-train representation using tensor cross interpolation. Particular emphasis is placed on a quantics time-difference formulation in which the required retarded convolutions are performed directly in quantics tensor-train form. Using controlled Gaussian benchmarks, we analyze the accuracy, bond dimensions, and computational scaling of the different approaches. We then validate the most promising formulations in self-consistent equilibrium and nonequilibrium DMFT calculations and demonstrate calculations up to the third order in the strong-coupling expansion. Finally, we extend the solver to impurity models with retarded density-density interactions and apply it within nonequilibrium extended DMFT. Our results show that tensor cross interpolation substantially reduces the cost of evaluating higher-order diagrams and provides a controlled, systematically improvable framework for nonequilibrium quantum impurity calculations.
