AI 中文总结
该研究构建含自洽非简谐性的离子晶格动力学平均场框架，将其与电子含时密度泛函理论对应，实现电子动力学研究进展向离子晶格的直接迁移。
AI 中文摘要
我们建立了一种平均场方法下的离子晶格动力学理论框架，其中通过自洽性引入非简谐性。在该图像中，三维空间内N个原子构成的多体系统动力学被映射为两类6N维矢量：描述平均原子位置演化的声子凝聚体，以及描述原子弹性常数演化的声子旋量。声子旋量由一个表现为自旋的量子数——声子赝自旋——来分类。多体刘维尔方程被替换为两个等价于密度泛函理论中电子波函数含时薛定谔方程的波动方程。利用这种平行性，我们构建了非简谐晶格的响应，使其与电子的含时密度泛函理论一一对应。与电子情况完全类似，我们用代表外场和力的算符矩阵元来表示离子响应。我们展示了非简谐性如何通过类哈特里-交换-关联核的声子机制屏蔽外扰动。我们给出了晶格光导率和热导率的表达式，表明热导率依赖于声子赝自旋。通过将密度矩阵近似为高斯型，我们得到了含时自洽简谐近似的方程。在该情况下，线性响应方程由包含三声子和四声子散射的非简谐核来表述。这项工作通过将非简谐晶格动力学转化为密度泛函理论的语言，证明了用于描述相互作用电子动力学响应的理论和计算进展可直接应用于相互作用离子的研究。
英文摘要
We establish a theoretical framework for the dynamics of a lattice of ions in a mean-field approach, where anharmonicity is included via self-consistency. In this picture, the many-body dynamics of a system of $N$ atoms in three dimensions is mapped onto two kinds of $6N$-dimensional vectors: the phonon condensate, describing the evolution of the average atomic positions, and the phonon spinors, describing the evolution of the atomic elastic constants. The phonon spinors are classified by a quantum number that behaves as a spin: the phonon pseudospin. The many-body Liouville equation is replaced by two wave equations equivalent to the time-dependent Schrödinger equation for the electronic wave function in density functional theory. Exploiting this parallelism, we formulate the response of the anharmonic lattice in one-to-one correspondence with time-dependent density functional theory for electrons. In complete analogy with the electronic case, we express the ionic response in terms of matrix elements of operators representing external fields and forces. We show how anharmonicity screens external perturbations through a phonon analogue of the Hartree-exchange-correlation kernel. We provide expressions for the lattice optical and thermal conductivity, showing how thermal conductivity depends on the phonon pseudospin. By approximating the density matrix as a Gaussian, we recover the equations of the time-dependent self-consistent harmonic approximation. In this case, the linear-response equations are formulated in terms of an anharmonic kernel including three- and four-phonon scattering. By translating anharmonic lattice dynamics into the language of density functional theory, this work shows how theoretical and computational advances in modeling the dynamical response of interacting electrons can be directly applied to interacting ions.
