Nature of symmetry breaking in the superconducting ground state
Nature of symmetry breaking in the superconducting ground state
复制标题
超导基态对称性破缺的本质
作者：
Kazue Matsuyama;J. Greensite
被认为是超导体中U(1)规范对称性破缺的序参数既是非定域的，又是规范相关的。因此，它们作为相结构的指南也是模棱两可的。我们指出，与非阿贝尔理论类似，局域U(1)规范对称性的整体子群可以看作只影响物质场的“守恒”对称性，并沿着我们先前工作的思路，构造了破坏这种对称性的规范不变判据。证明了守恒对称性自发破缺是任一给定规范中(阿贝尔或非阿贝尔)规范群的整体子群存在自发对称性破缺的必要条件，也是该规范群的整体子群在某种规范下存在自发破缺的充分条件。作为说明，我们在晶格版本的Ginzburg-Landau模型中数值计算了理论的相边界和与每一相中的各种对称性相关的序参数。
The order parameters which are thought to detect U(1) gauge symmetry breaking in a superconductor are both nonlocal and gauge dependent. For that reason, they are also ambiguous as a guide to phase structure. We point out that a global subgroup of the local U(1) gauge symmetry may be regarded, in analogy to non-Abelian theories, as a “custodial” symmetry affecting the matter field alone, and construct, along the lines of our previous work, a gauge-invariant criterion for breaking symmetries of this kind. It is shown that spontaneous breaking of custodial symmetry is a necessary condition for the existence of spontaneous symmetry breaking of a global subgroup of the (Abelian or non-Abelian) gauge group in any given gauge, and a sufficient condition for the existence of spontaneous breaking of a global subgroup of the gauge group in some gauge. As an illustration, we compute numerically, in a lattice version of the Ginzburg-Landau model, the phase boundaries of the theory and the order parameters associated with various symmetries in each phase.