Complexity growth in Gubser–Rocha models with momentum relaxation

The Einstein–Maxwell–Axion–Dilaton (EMAD) theories, based on the Gubser–Rocha (GR) model, are very interesting in holographic calculations of strongly correlated systems in condensed matter physics. Due to the presence of spatially dependent massless axionic scalar fields, the momentum is relaxed, and we have no translational invariance at finite charge density. It would be of interest to study some aspects of quantum information theory for such systems in the context of AdS / CFT where EMAD theory is a holographic dual theory. For instance, in this paper we investigate the complexity and its time dependence for charged AdS black holes of EMAD theories in diverse dimensions via the complexity equals action (CA) conjecture. We will show that the growth rate of the holographic complexity violates Lloyd’s bound at finite times. However, as shown at late times, it depends on the strength of the momentum relaxation and saturates the bound for these black holes.