Chiral Sachdev-Ye model: Integrability and chaos of anyons in 1+1d

We construct and study a chiral Sachdev-Ye (SY) model consisting of N chiral SU(M)₁ Wess-Zumino-Witten (WZW) models with current-current interactions among each other, which generalizes the 0+1d quantum chaotic SY spin model into 1+1d chiral system with anyon excitations. Each WZW model hosts Abelian anyons as charge excitations, and may arise as the chiral edge theory of 2+1d gapped topological phases. We solve the chiral SY model in two limits which show distinct quantum dynamics. The first limit is the case with uniform interactions at any integers N and M, which is integrable and decomposes into a chiral SU(M)_N WZW model and its coset with different "speed of light". When N=M=2, the model maps to a free Majorana fermion model. The second limit is the large N and M limit with random interactions, which is solvable to the leading frac{1}{NM} order, and exhibits many-body quantum chaos in the out-of-time-ordered correlation of anyons. As the interaction strength approaches the upper limit preserving the chirality, the leading velocity-dependent Lyapunov exponent of the model saturates the maximal chaos bound 2π/β at temperature β^-1.