Complexity and phase transitions in a holographic QCD model

TL;DR

This paper investigates how the growth rate of holographic complexity behaves near phase transitions in a QCD model, revealing it can characterize the transition type and satisfy Lloyd's bound.

Contribution

It demonstrates that holographic complexity growth rate signals phase transition types in a holographic QCD model, providing a new diagnostic tool.

Findings

Complexity growth rate drops or jumps near critical points.

Behavior of complexity near critical temperature characterizes transition type.

Lloyd's bound is satisfied, saturated only in the conformal case.

Abstract

Applying the "Complexity=Action" conjecture, we study the holographic complexity close to crossover/phase transition in a holographic QCD model proposed by Gubser et al. This model can realize three types of phase transition, crossover or first and second order, depending on the parameters of the dilaton potential. The re-scaled late-time growth rate of holographic complexity density for the three cases is calculated. Our results show that it experiences a fast drop/jump close to the critical point while approaching constants far beyond the critical temperature. Moreover, close to the critical temperature, it shows a behavior characterizing the type of the transition. These features suggest that the growth rate of the holographic complexity may be used as a good parameter to characterize the phase transition. The Lloyd's bound is always satisfied for the cases we considered but only saturated for the conformal case.