论文标题
$ u（1）$对称的耦合复杂模型的自发断裂
Spontaneous Breaking of $U(1)$ Symmetry in Coupled Complex SYK Models
论文作者
论文摘要
如[1]中所示，大型$ n $ n $ majorana syk型号的两个副本可以自发破坏$ z_2 $对称时，当它们与适当的四分之一术语结合时。在本文中，我们类似地研究了复杂的SYK模型的两个副本，该副本由保留$ u（1）\ times u（1）$对称的四分之一术语结合。我们还提出了该耦合模型的张量对应物。当四分之一术语的系数$α$处于一定范围内时，耦合的大$ n $理论几乎是顺式的。我们将费米恩双线运算符的缩放维度计算为$α$的函数。我们表明，操作员$ c_ {1i}^\匕首c_ {2i} $，该{2i} $在轴向$ u（1）$对称下收取，在固定点线之外获得了一个复杂的维度。我们得出了大型$ n $ dyson-schwinger方程，并表明，在固定线之外，此$ u（1）$对称性在低温下自发损坏，因为该操作员获得了期望值。我们通过推断到大$ n $的精确对角线化来支持这些发现。
As shown in [1], two copies of the large $N$ Majorana SYK model can produce spontaneous breaking of a $Z_2$ symmetry when they are coupled by appropriate quartic terms. In this paper we similarly study two copies of the complex SYK model coupled by a quartic term preserving the $U(1) \times U(1)$ symmetry. We also present a tensor counterpart of this coupled model. When the coefficient $α$ of the quartic term lies in a certain range, the coupled large $N$ theory is nearly conformal. We calculate the scaling dimensions of fermion bilinear operators as functions of $α$. We show that the operator $c_{1i}^\dagger c_{2i}$, which is charged under the axial $U(1)$ symmetry, acquires a complex dimension outside of the line of fixed points. We derive the large $N$ Dyson-Schwinger equations and show that, outside the fixed line, this $U(1)$ symmetry is spontaneously broken at low temperatures because this operator acquires an expectation value. We support these findings by exact diagonalizations extrapolated to large $N$.
