AI 中文总结
本文将量子张量交叉插值用于变量分离框架，缓解高阶强耦合展开的高维积分挑战，实现最高四阶自洽稳态DMFT计算，还分析了非相互作用极限下强耦合展开的收敛性并观测到渐近区起始。
AI 中文摘要
实时杂质求解器可在动力学平均场理论（DMFT）框架内研究输运现象并描述非平衡晶格系统，还能直接获取平衡与非平衡系统的谱函数。自洽强耦合展开是广泛应用的方法，其最低阶实现对应非交叉近似，但高阶实现计算量极大——图拓扑的数量随展开阶数呈阶乘增长，而自能和格林函数的计算需要越来越高维的积分。本文证明，在变量分离框架中采用量子张量交叉插值（quantics tensor cross interpolation）可缓解后一挑战。与此前使用的尺度分离方法相比，新方案的键维数显著降低，支持最高至四阶的自洽稳态DMFT计算。我们通过平衡系统和光掺杂系统的代表性结果展示其性能，还通过计算至六阶的图分析了强耦合展开在具挑战性的非相互作用极限下的收敛性。在该阶，强耦合展开渐近区的起始变得明显，这使得外推技术的应用成为可能。
英文摘要
Real-time impurity solvers enable the study of transport phenomena and the description of nonequilibrium lattice systems within the framework of dynamical mean-field theory (DMFT). They also provide direct access to the spectral functions of both equilibrium and nonequilibrium systems. A widely used approach is the self-consistent strong-coupling expansion, whose lowest-order implementation corresponds to the non-crossing approximation. Higher-order implementations, however, are computationally demanding because the number of diagram topologies grows factorially with expansion order, while the evaluation of self-energies and Green's functions requires increasingly high-dimensional integrations. Here, we demonstrate that the latter challenge can be mitigated by employing quantics tensor cross interpolation in a variable-separated framework. Compared with the previously used scale-separated approach, the new scheme yields substantially lower bond dimensions and capacitates self-consistent steady-state DMFT calculations up to fourth order. We illustrate its performance with representative results for both equilibrium and photo-doped systems. In addition, we analyze the convergence of the strong-coupling expansion in the challenging noninteracting limit by computing diagrams up to sixth order. At this order, the onset of the asymptotic regime of the strong-coupling expansion becomes apparent, which allows the application of extrapolation techniques.
Comments11 pages, 10 figures
