Operator growth in SU(2) Yang-Mills theory

Krylov complexity is a novel observable for detecting quantum chaos, and an indicator of a possible gravity dual. In this paper, we compute the Krylov complexity and the associated Lanczos coefficients in the SU(2) Yang-Mills theory, which can be reduced to a nonlinearly coupled harmonic oscillators (CHO) model. We show that there exists a chaotic transition in the growth of Krylov complexity. The Krylov complexity shows a quadratic growth in the early time stage and then grows linearly. The corresponding Lanczos coefficient satisfies the universal operator growth hypothesis, i.e., grows linearly first and then enters the saturation plateau. By the linear growth of Lanczos coefficients, we obtain an upper bound of the quantum Lyapunov exponent. Finally, we investigate the effect of different energy sectors on the K-complexity and Lanczos coefficients.