虚磁场作用下BCS模型中的超导相
Superconducting phase in the BCS model with imaginary magnetic field
摘要：
我们证明了在具有虚外磁场的约化四次BCS模型中，存在自发的U（1）对称破缺（SSB）和非对角长程序（ODLRO）.该系统被定义在一个超立方晶格与周期性的边界条件，在正温度。在哈密顿量的自由部分，我们假设最近邻跳跃。化学势是固定的，因此自由费米面不会退化。表示电子自旋和虚外部磁场之间相互作用的项是自旋算符的z分量乘以纯虚参数。SSB和ODLRO显示在无限体积极限的热平均在整个费米福克空间。负耦合常数的大小必须大于某个值，这样间隙方程才是可解的。由于虚磁场的存在，气隙方程不同于传统的平均场BCS模型。通过调整虚磁场，该模型显示了高温下的SSB和ODLRO，弱耦合制度，其中传统的简化BCS模型没有显示这些现象。证明是基于格拉斯曼高斯积分公式和双尺度积分计划，以分析控制的配方。
英文摘要：
We prove that in the reduced quartic BCS model with an imaginary external magnetic field a spontaneous U(1)-symmetry breaking (SSB) and an off-diagonal long range order (ODLRO) occur. The system is defined on a hyper-cubic lattice with periodic boundary conditions at positive temperature. In the free part of the Hamiltonian we assume the nearest-neighbor hopping. The chemical potential is fixed so that the free Fermi surface does not degenerate. The term representing the interaction between electrons' spin and the imaginary external magnetic field is the z-component of the spin operator multiplied by a pure imaginary parameter. The SSB and the ODLRO are shown in the infinite-volume limit of the thermal average over the full Fermionic Fock space. The magnitude of the negative coupling constant must be larger than a certain value so that the gap equation is solvable. The gap equation is different from that of the conventional mean field BCS model because of the presence of the imaginary magnetic field. By adjusting the imaginary magnetic field this model shows the SSB and the ODLRO in high temperature, weak coupling regimes where the conventional reduced BCS model does not show these phenomena. The proof is based on Grassmann Gaussian integral formulations and a double-scale integration scheme to analytically control the formulations.
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