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arXiv 1905.09406cond-mat.supr-conhep-lathep-th
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超导基态对称性破缺的性质

The nature of symmetry breaking in the superconducting ground state

Kazue Matsuyama, Jeff Greensite

摘要:

用来检测超导体中U(1)规范对称性破缺的序参量是非定域的和规范相关的。由于这个原因,它们作为相结构的指导也是模糊的。我们指出,局部U(1)规范对称性的整体子群可以被看作是一种只影响物质场的“监护”对称性,与非阿贝尔理论类似,并沿着我们以前工作的路线,构造了一个新的规范不变的判据,用于破缺这类对称性。研究表明,保管对称性自发破缺是(阿贝尔或非阿贝尔)规范群的整体子群在任意给定规范下存在自发对称性破缺的必要条件,也是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.作为一个例子,我们计算数值,在格点版本的Ginzburg-Landau模型,相边界的理论和序参量与各种对称性在每个阶段。

英文摘要:

The order parameters which are thought to detect U(1) gauge symmetry breaking in a superconductor are both non-local 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 new 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 the lattice version of the Ginzburg-Landau model, the phase boundaries of the theory and the order parameters associated with various symmetries in each phase.

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