A melonic quantum mechanical model without disorder

A

bstract

We consider a quantum mechanical model involving interacting fermions without disorder that has the same low energy physics as the supersymmetric SYK model. The model is SU(2) invariant, and the supercharge involves the SU(2) 3j symbol. We analyze various solvable corners, conceptually explain why it has a melonic expansion, and perform an exact diagonalization for small values of N . Expanded around the states with maximal angular momentum, the model is approximated by a two dimensional CFT. The BPS states have a simple description in that regime.