Discoveries / mathematical-physics

Sharp Bounds on the Ground State Energy of the SYK Model

For the Sachdev-Ye-Kitaev Hamiltonian on $n$ Majorana modes with $k$-body interactions, the paper proves $\mathbb{E}\|H\|_{op} = (1-o(1))\sqrt{2n}/k$ for super-constant $k \le o(\sqrt{n})$, confirming predictions of Garcia-Garcia, Jia and Verbaarschot and answering a question of Feng, Tian and Wei.