Universal scrambling in gapless quantum spin chains

Information scrambling, characterized by the out-of-time-ordered correlator (OTOC), has recently attracted much attention, because it sheds new light on chaotic dynamics on quantum many-body systems. As an important feature of OTOC, its decay rate has an upper bound, which is referred to as the chaotic bound. The scale invariance, which appears near the quantum critical region in condensed matter physics, is considered to be important for the fast decay of OTOC.

In this study, we focus on the one-dimensional spin-1/2 antiferromagnetic XXZ model and investigate the relationship between scrambling and the scale invariance. As an indicator of the scrambling, we adopt the averaged OTOC, which is related to the operator space entanglement entropy (OSEE). We numerically calculate time-dependence of the OSEE in the early-time region in the thermodynamic limit by using the infinite time-evolving block decimation method. Our numerical results suggest that the scale invariance leads to a universal behavior of the OTOC that is independent of the anisotropic parameter, which reflects the universality of the two-dimensional conformal field theory with the conformal charge c=1 at low temperatures.

Reference
S. Nakamura, E. Iyoda, T. Deguchi, and T. Sagawa, Phys. Rev. B 99, 224305 (2019)