论文标题
Nambu-Goldstone模式用于超导晶格费米子
Nambu-Goldstone Modes for Superconducting Lattice Fermions
论文作者
论文摘要
我们提出了一个晶格模型，用于超导式费米子，其最接近的两体相互作用是Bardeen-cooper-schrieffer型配对，在超我们的晶格$ \ mathbb {z}^d $与dimension $ d \ ge 3 $ 3 $上。尽管认为两个电子之间的这些有效的相互作用是由电子 - 音波相互作用引起的，但我们假设两个电子之间的相互作用是没有声子的短范围。对于该模型，我们证明了在低温下超导性的远距离顺序的存在，并且还证明了在无限量 - 体积基态之上的无间隙激发。也就是说，出现了与U（1）对称性破坏相关的Nambu-Goldstone模式。相应的nambu-goldstone玻色子正是库珀对，由上下电子组成。
We present a lattice model for superconducting fermions whose nearest-neighbour two-body interactions are a Bardeen-Cooper-Schrieffer-type pairing on the hypercubic lattice $\mathbb{Z}^d$ with the dimension $d\ge 3$. Although these effective interactions between two electrons are believed to be caused by electron-phonon interactions, we assume that the interactions between two electrons are of short range without phonons. For the model, we prove the existence of the long-range order of the superconductivity at low temperatures, and also prove the existence of a gapless excitation above the infinite-volume ground state. Namely, there appears a Nambu-Goldstone mode which is associated with the U(1) symmetry breaking. The corresponding Nambu-Goldstone boson is exactly a Cooper pair, which consists of spin up and down electrons.
