Lieb-Robinson bound in one-dimensional inhomogeneous quantum systems

Lieb-Robinson bound (LRB) in one-dimensional noninteracting many-electron systems with the disordered and quasiperiodic on-site potentials is studied numerically. For the short-range hopping system, a logarithmic light cone (i.e. |x| = beta log t + x(0)) is found in the system with the disordered on-site potential for small time. The coefficient fi decreases with the increasing strength of disordered. When time is large, the bound does not change with time (i.e. |x| = C). For the generalized Fibonacci quasiperiodic (GFQ) system, the on-site potential is taken as V or -V according to two kinds of GFQ sequences. It is found that the system has a power-law light cone (i.e. |x| proportional to t(gamma), with 0 < gamma < 1). The exponent gamma decreases with the increasing V. We also find that gamma for the first class of GFQ system is larger than that for the second class of GFQ system with the same V. Finally, the effects of the long-range hopping which decays like r(-alpha) with the distance r on LRB are discussed.

Automated summary

The Lieb-Robinson bound (LRB) is numerically studied in one-dimensional noninteracting many-electron systems with disordered and quasiperiodic on-site potentials. For the short-range hopping system, a logarithmic light cone is found in the presence of a disordered on-site potential, which decreases with increasing disorder strength. In the long time limit, the bound does not change with time. For the generalized Fibonacci quasiperiodic system, a power-law light cone is observed, with the exponent decreasing as the strength of the potential increases. It is also found that the exponent is larger for the first class of GFQ system compared to the second class with the same potential. Lastly, the effects of long-range hopping on the LRB are discussed.