超导晶格费米子的Nambu-Goldstone模
Nambu-Goldstone Modes for Superconducting Lattice Fermions
摘要：
本文提出了一个超导费米子的晶格模型，它的最近邻两体相互作用是超立方晶格$\mathbb{Z}^d$上的Bardeen-Cooper-Schriffel型对，维数为$d\ge 3$ .虽然两个电子之间的这些有效相互作用被认为是由电子-声子相互作用引起的，但我们假设两个电子之间的相互作用是没有声子的短程相互作用。对于该模型，我们证明了低温下超导电性的长程序的存在，并且证明了在无限体积基态之上的无隙激发的存在。也就是说，出现了与U（1）对称性破缺有关的Nambu-Goldstone模。相应的南武-戈德斯通玻色子就是一个库珀对，它由自旋向上和向下的电子组成。
英文摘要：
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.
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