Asymmetric quantum information scrambling in inhomogeneous XXZ spin chains

Abstract

Inhomogeneous systems have become increasingly relevant in experimentally engineered quantum many-body systems, where spatially varying interaction strengths can significantly influence nonequilibrium dynamics. Motivated by this, we numerically study the out-of-time-ordered correlators (OTOCs) in inhomogeneous XXZ spin chains. Using two types of spatially varying interaction profiles, namely, linear-gradient and stepwise profiles, we show that spatial inhomogeneity in the interactions can induce pronounced asymmetry in information scrambling, with OTOC operators located at different sites exhibiting distinct dynamical behavior. In particular, OTOCs associated with the strongly interacting side exhibit suppressed scrambling compared to those associated with the weakly interacting side, with the difference becoming more pronounced when the interaction strengths differ significantly. To elucidate the origin of the long-time saturation of OTOCs, we analyze the diagonal matrix elements of the OTOC observables in the energy eigenbasis and their overlap with the Hamiltonian, which explicitly incorporates the spatial interaction profile. The resulting analytical expression is consistent with the numerical results. Finally, we extend our analysis to periodically driven inhomogeneous spin chains and show that the interaction-gradient-induced asymmetry persists under periodic driving.