论文标题
Migdal-Eliashberg理论作为经典自旋链
Migdal-Eliashberg theory as a classical spin chain
论文作者
论文摘要
我们通过将自由能映射到Zeeman磁场中的Heisenberg Spin链中，以经典的自旋映射到Zeeman磁场中的电子旋转来制定电子波相互作用的Migdal-Eliashberg理论。自旋成分是能量集成正常和异常的绿色功能，而链的位置是费米子毛的频率。 Zeeman场与自旋坐标线性生长，并与铁磁性自旋旋转相互作用竞争，该相互作用作为反向距离的平方落下。自旋链表示使一系列以前未知的属性都可以看见。特别是，在强耦合时出现了埃里亚斯贝格方程的许多新解。自由能功能的这些鞍点对应于旋转翻转。我们认为它们也是动力学方程的固定点，并且在远离强耦合超导体的平衡动力学中起着至关重要的作用。直到整个阶段，最小化自由能的频率依赖性差距函数必须是非负的。我们的Eliashberg旋转和Anderson Pseudospins之间存在很强的相似之处，尽管这两套旋转从来没有重合。
We formulate the Migdal-Eliashberg theory of electron-phonon interactions in terms of classical spins by mapping the free energy to a Heisenberg spin chain in a Zeeman magnetic field. Spin components are energy-integrated normal and anomalous Green's functions and sites of the chain are fermionic Matsubara frequencies. The Zeeman field grows linearly with the spin coordinate and competes with ferromagnetic spin-spin interaction that falls off as the square of the inverse distance. The spin-chain representation makes a range of previously unknown properties plain to see. In particular, infinitely many new solutions of the Eliashberg equations both in the normal and superconducting states emerge at strong coupling. These saddle points of the free-energy functional correspond to spin flips. We argue that they are also fixed points of kinetic equations and play an essential role in far from equilibrium dynamics of strongly coupled superconductors. Up to an overall phase, the frequency-dependent gap function that minimizes the free energy must be non-negative. There are strong parallels between our Eliashberg spins and Anderson pseudospins, though the two sets of spins never coincide.
