论文标题
高阶辅助场量子蒙特卡洛法
Higher Order Auxiliary Field Quantum Monte Carlo Methods
论文作者
论文摘要
很长一段时间以来，辅助场量子蒙特卡洛（AFQMC）方法一直是强相关电子领域的主力，并且在ALF软件包（https://alf.physik.uni-wuerzburg.de）中发现了其最新的实现。将猪肉分解的利用与非相互作用的汉密尔顿分解相互作用使这种方法固有地从虚构的时间切片来固有地二阶。我们表明，由于使用Hubbard-Stratonovich转换（HST），因此对时间演化进行了半群结构，因此需要引入新的复杂 - 温米特分裂方法，以便达到更高阶段。我们将举例说明这些新方法并研究它们的效率，并与AFQMC方法领域中其他已建立的第二和高阶方法进行比较。
The auxiliary field quantum Monte Carlo (AFQMC) method has been a workhorse in the field of strongly correlated electrons for a long time and has found its most recent implementation in the ALF package (https://alf.physik.uni-wuerzburg.de). The utilization of the Trotter decomposition to decouple the interaction from the non-interacting Hamiltonian makes this method inherently second order in terms of the imaginary time slice. We show that due to the use of the Hubbard-Stratonovich transformation (HST) a semigroup structure on the time evolution is imposed that necessitates the introduction of a new family of complex-hermitian splitting methods for the purpose of reaching higher order. We will give examples of these new methods and study their efficiency, as well as perform comparisons with other established second and higher order methods in the realm of the AFQMC method.
