Spontaneous breaking of U(1) symmetry in coupled complex SYK models
Spontaneous breaking of U(1) symmetry in coupled complex SYK models
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DOI：
10.1007/jhep11(2020)162
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发表时间：
2020-06
影响因子：
5.4
通讯作者：
I. Klebanov;A. Milekhin;G. Tarnopolsky;Wenli Zhao
中科院分区：
文献类型：
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作者：
I. Klebanov;A. Milekhin;G. Tarnopolsky;Wenli Zhao
如 [1] 所示，大 N Majorana SYK 模型的两个副本在通过适当的四次项耦合时可以产生 Z 2 对称性的自发破缺。在本文中，我们类似地研究了复杂 SYK 模型的两个副本，通过保留 U (1)× U (1) 对称性的四次项耦合。我们还提出了该耦合模型的张量对应项。当四次项的系数α在一定范围内时，耦合大N理论接近共形。我们将费米子双线性算子的缩放维数计算为 α 的函数。我们证明，在轴 U (1) 对称性下充电的算子获得了不动点线之外的复维度。我们推导了大 N Dyson-Schwinger 方程，并表明，在固定线之外，这种 U (1) 对称性在低温下会自发破缺，因为该算子获得了期望值。我们通过外推到大 N 的精确对角化来支持这些发现。
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)× 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, 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.