Spontaneous Breaking of U(1) Symmetry in Coupled Complex Sachdev-Ye-Kitaev Models*

We study two copies of the complex SYK model coupled by a quartic term preserving the U (1) × U (1) symmetry. When the coupling coefficient α lies in a certain range, the large N theory is nearly conformal. We derive the large N Dyson-Schwinger equations and show that for the coupling α outside this range, the axial U(1) symmetry is spontaneously broken at low temperatures. We support these findings by exact diagonalizations extrapolated to large N.