Transverse Goldstone Mode In Holographic Fluids With Broken Translations

The study of strongly coupled systems has long been an important research direction at the frontier of condensed matter physics.However,most of conventional condensed matter theories are mainly based on perturbative methods which fail to describe systems in the strongly coupled regions.The string inspired holographic duality(also known as the Ad S/CFT duality)links a strongly coupled quantum field theory with a classical gravity in one dimension higher,providing a new perspective and approach to understanding the physics of various strongly coupled systems.In past two decades,this duality has been widely applied to high energy physics,condensed matter physics as well as quantum information.In this paper,we focus on low-energy excitations in liquid systems with spontaneously broken translations using the holographic method.In introduction,we briefly introduce the effective field theory of fluids and their main features.In Chapter 1,the holographic nature of gravity and the Ad S/CFT duality are introduced.In Chapter 2,we review the simplest holographic axion model and its application to solids.In chapter 3,we focus on the low energy transverse excitations in liquid systems with spontaneously broken translations by using a specific holographic model.Firstly,It is found that,in the absence of momentum relaxation,there exist two decoupled gapless modes in the transverse channel,one of which is a purely diffusive mode that is associated with the conserved momentum and the other corresponds to vortex like excitations,which can be viewed as the Goldstone mode of spontaneous symmetry breaking.Then,we break translations explicitly by turning on an external source.When the symmetry breaking is weak,the would-be gapless modes both get relaxed and acquire a tiny mass gap.However,when the symmetry breaking is strong,there exists a(pseudo-)diffusiveto-sound crossover that is set by a momentum gap.