论文标题
$π$通量阶段和晶格费米斯的超导性与古典轨迹磁场耦合
$π$ Flux Phase and Superconductivity for Lattice Fermions Coupled to Classical Gauge Fields
论文作者
论文摘要
我们研究了与经典仪表磁场相连的超导晶格费米子。也就是说，没有规格场，晶格费米子显示了超导的远程顺序。在上一篇论文中，本作者证明了远程顺序的存在。本文是上一篇的持续部分。更准确地说，fermions之间的相互作用被认为是Bardeen-cooper-schrieffer型配对，它是高皮块晶格$ \ mathbb {z}^d $的最接近的邻居两体相互作用，带有尺寸$ d \ ge 3 $。在本文中，我们通过引入古典U（1）仪表字段来处理相应的测量模型。我们证明，量规场的一定配置可产生$π$通量，用于晶格中所有斑点的$π$通量，最大程度地减少了费米昂系统的地面能量。由于仪表字段的这种配置与上一篇论文的哈密顿量的跳跃幅度完全吻合，因此整个系统的基态状态显示了超导远程顺序。仪表字段的任何配置与量规场的特殊配置等效的量规场也产生了另一个基态。但是，如果库珀对相关性在量规等级类别上平均，那么除了现场相关性外，它们正在消失，因为库珀对的相关性不一定是不一定的。另一方面，量规不间断的弦库珀对相关始终显示出相同的远程顺序，以适用于量规等级类中任何规格字段的配置。
We study superconducting lattice fermions coupled to classical gauge fields. Namely, without the gauge fields, the lattice fermions show superconducting long-range order. In the previous paper, the existence of the long-range order was proved by the present author. This paper is the continuing part of the previous one. More precisely, the interactions between fermions were assumed to be a Bardeen-Cooper-Schrieffer-type pairing which is a nearest-neighbour two-body interaction on the hypercubic lattice $\mathbb{Z}^d$ with the dimension $d\ge 3$. In the present paper, we deal with the corresponding gauged model by introducing classical U(1) gauge fields. We prove that a certain configuration of gauge fields which yields the $π$ flux for all the plaquettes in the lattice minimizes the ground-state energy of the fermion system. Since this configuration of the gauge fields exactly coincides with the hopping amplitudes of the Hamiltonian of the previous paper, the ground state of the whole system shows superconducting long-range order. Any configuration of gauge fields which is gauge-equivalent to this special configuration of the gauge fields also yields another ground state. However, if the Cooper pair correlations are averaged over the gauge-equivalent class, then they are vanishing except for the on-site correlation because the Cooper pair correlations are not necessarily gauge invariant. On the other hand, the string Cooper pair correlations which are gauge invariant always show the same long-range order for any configuration of gauge fields in the gauge-equivalent class.
