Montoya-Castillo Andrés, Markland Thomas E
Department of Chemistry, Stanford University, Stanford, California, 94305, USA.
Sci Rep. 2018 Aug 28;8(1):12929. doi: 10.1038/s41598-018-31162-6.
We derive a rigorous, quantum mechanical map of fermionic creation and annihilation operators to continuous Cartesian variables that exactly reproduces the matrix structure of the many-fermion problem. We show how our scheme can be used to map a general many-fermion Hamiltonian and then consider two specific models that encode the fundamental physics of many fermionic systems, the Anderson impurity and Hubbard models. We use these models to demonstrate how efficient mappings of these Hamiltonians can be constructed using a judicious choice of index ordering of the fermions. This development provides an alternative exact route to calculate the static and dynamical properties of fermionic systems and sets the stage to exploit the quantum-classical and semiclassical hierarchies to systematically derive methods offering a range of accuracies, thus enabling the study of problems where the fermionic degrees of freedom are coupled to complex anharmonic nuclear motion and spins which lie beyond the reach of most currently available methods.
我们推导出了一个严格的、将费米子产生和湮灭算符映射到连续笛卡尔变量的量子力学映射，它能精确再现多费米子问题的矩阵结构。我们展示了我们的方案如何用于映射一般的多费米子哈密顿量，然后考虑两个编码多费米子系统基本物理的特定模型，即安德森杂质模型和哈伯德模型。我们用这些模型展示了如何通过明智地选择费米子的指标排序来构建这些哈密顿量的高效映射。这一进展提供了一条计算费米子系统静态和动态性质的替代精确途径，并为利用量子 - 经典和半经典层次结构系统地推导具有一系列精度的方法奠定了基础，从而能够研究费米子自由度与复杂非谐核运动和自旋耦合的问题，而这些问题是目前大多数可用方法无法解决的。
