晶格上的量子电动力学含时密度泛函理论
Quantum electrodynamical time-dependent density functional theory on a lattice
摘要：
我们提出了一个严格的含时密度泛函理论的相互作用晶格电子强耦合腔光子。我们从一个例子开始，一个粒子的哈伯德二聚体耦合到一个单一的光子模式，这是等效的单模自旋玻色子模型或量子拉比模型。对于这个系统，我们证明了在初始态和密度满足一定条件的情况下，电子-光子波函数是电子密度和光子坐标期望值的唯一泛函.然后，我们推广的形式主义，许多相互作用的电子在一个晶格耦合到多个光子模式，并证明了一般的映射定理。我们还表明，从基态的晶格哈密顿系统的任何密度连续的二阶导数是本地$v$ -representable。
英文摘要：
We present a rigorous formulation of the time-dependent density functional theory for interacting lattice electrons strongly coupled to cavity photons. We start with an example of one particle on a Hubbard dimer coupled to a single photonic mode, which is equivalent to the single mode spin-boson model or the quantum Rabi model. For this system we prove that the electron-photon wave function is a unique functional of the electronic density and the expectation value of the photonic coordinate, provided the initial state and the density satisfy a set of well defined conditions. Then we generalize the formalism to many interacting electrons on a lattice coupled to multiple photonic modes and prove the general mapping theorem. We also show that for a system evolving from the ground state of a lattice Hamiltonian any density with a continuous second time derivative is locally $v$-representable.
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