费米型级联运动方程的绝热截断方案

Adiabatic Terminator for Fermionic Hierarchical Equations of Motion

研究开放量子系统的量子耗散动力学对于理解许多新奇量子现象背后的机制和实现量子器件的精确量子态控制具有重要意义.级联运动方程方法已成为研究这类量子耗散动力学最常用的数值方法之一.然而,在处理强电子关联系统时,准确描述强关联效应需要高的级联截断层数.这导致级联运动方程方法需要耗费大量物理内存和计算时间.为了解决该问题,将具有最快耗散速率的耗散模式与其他较慢的耗散模式分离,提出了一种级联运动方程的绝热截断方案.在单杂质安德森模型上进行的数值测试表明,与传统的方案相比,该截断方案显著地降低了级联运动方程收敛需要的截断层数.此外,该截断方案缓解了长时间耗散动力学中的数值不稳定性.

The hierarchical equation of motion method has become one of the most popular numerical methods for describing the dissipative dynamics of open quantum systems linearly coupled to environment.However,its applications to systems with strong electron correlation are largely restrained by the computational cost,which is mainly caused by the high truncation tier L required to accurately characterize the strong correlation effect.In this work,we develop an adiabatic terminator by decoupling the principal dissipation mode with the fastest dissipation rate from the slower ones.The adiabatic terminator leads to substantially enhanced convergence with respect to L as demonstrated by the numerical tests carried out on a single impurity Anderson model.Moreover,the adiabatic terminator alleviates the numerical instability problems in the long-time dissipative dynamics.