SYK-like tensor quantum mechanics with Sp(N) symmetry

We introduce a family of tensor quantum-mechanical models based on irreducible rank-3 representations of Sp(N). In contrast to irreducible tensor models with O(N) symmetry, the fermionic tetrahedral interaction does not vanish and can therefore support a melonic large N limit. The strongly-coupled regime has a very analogous structure as in the complex SYK model or in U(N) x O(N) x U(N) tensor quantum mechanics, the main difference being that the states are now singlets under Sp(N). We introduce character formulas that enumerate such singlets as a function of N, and compute their first values. We conclude with an explicit numerical diagonalization of the Hamiltonian in two simple examples: the symmetric model at N = 1, and the antisymmetric traceless model at N = 3. (C) 2019 The Author(s). Published by Elsevier B.V.