Complexity growth in Gubser-Rocha models with momentum relaxation

TL;DR

This paper studies how the growth of holographic complexity in Gubser-Rocha models with momentum relaxation behaves over time, revealing violations and eventual saturation of Lloyd's bound depending on relaxation strength.

Contribution

It investigates the time evolution of holographic complexity in EMAD theories with momentum relaxation, showing how it violates and then saturates Lloyd's bound.

Findings

Complexity growth rate violates Lloyd's bound at finite times.

At late times, the growth rate depends on momentum relaxation strength.

The growth rate saturates the bound for strong momentum relaxation.

Abstract

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 the 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 the Lloyd's bound at finite times. However, as shown at late times, it depends on the strength of momentum relaxation and saturates the bound for these black holes.