Quantum information stored in local operators spreads over other degrees of freedom of the system during time evolution, known as scrambling. This process is conveniently characterized by the out-of-time-order commutator (OTOC), the time dependence of which reveals salient aspects of the system's dynamics. Here we study the spatially local spin-correlation function, i.e., the expectation value of the spin commutator and the corresponding OTOC of Dirac-Weyl systems in one, two, and three spatial dimensions. The OTOC can be written as the square of the expectation value of the commutator and the variance of the commutator. In principle, the problem features two energy scales, the chemical potential and the high-energy cutoff. We find that only the latter is dominant, therefore the time evolution is separated into only two different regions. The spin-correlation function grows linearly with time initially and decays as t-2 for late times. The OTOC reveals a universal t2 initial growth from both the commutator and the variance while its late time decay t-2 originates from the variance of the commutator. This late time decay is identified as a characteristic signature of Dirac-Weyl fermions. These features remain present also at finite temperatures. Our results indicate that Dirac-Weyl systems are slow information scramblers and are essential when additional channels for scrambling, i.e., interaction and disorder, are analyzed.
ASJC Scopus subject areas
- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics