Scrambling and chaos in quantum spin chains: insights from matrix product states

We develop an approach to investigate scrambling, as measured by out-of-time-order correlators (OTOCs), in one-dimensional quantum systems. The approach is based on thermofield double states and is closely related to the standard purification method for the simulation of finite-temperature equilibrium properties using matrix product states. However, it presents a number of computational advantages which we detail here. We apply the method to the paradigmatic 1D quantum Heisenberg model and evaluate its OTOCs for different spin representations S up to 5. The explicit treatment of the non-Abelian SU(2) symmetry allows to compute OTOCs for intermediate time scales and large system sizes. As S increases we find a "quantum to classical" crossover where the OTOCs starts to exhibit a period of exponential growth with a Lyapunov exponent λ_L, thus corroborating a recent conjecture in the literature.