A melonic quantum mechanical model without disorder

TL;DR

This paper introduces a disorder-free, $SU(2)$ invariant quantum fermion model with low energy behavior similar to the SYK model, featuring a melonic expansion and connections to a 2D conformal field theory.

Contribution

It presents a novel fermionic quantum model without disorder that replicates SYK-like physics and analyzes its solvable limits and low-energy conformal structure.

Findings

Model exhibits melonic expansion

Exact diagonalization performed for small N

Approximate 2D CFT description around maximal angular momentum states

Abstract

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.