Many-body chaos in a conformal gauge theory*

The onset of many-body quantum chaos in fermionic systems can be diagnosed from the growth of initally anticommuting fermion field operators. We compute such anti-commutators of fermion field operators in (2 + 1)d U (1) gauge theory with N_f flavors of fermions to leading order in 1/N_f . For large enough N_f , this is an interacting conformal field theory and describes the low energy properties of the Dirac spin liquid. The anticommutator grows exponentially in time with a rate defined by the Lyapunov exponent λ_L and grows ballistically in space at a speed identified as the “butterfly velocity” v_B. The scaling with temperature is fixed by conformal invariance. We briefly comment on the growth of local current operators and the breakdown of the large N_f expansion.