AdS/CFT Duality And Its Application In Condensed Matter Physics

Anti de-Sitter/Conformal Field Theory (AdS/CFT) duality is developed from the frameworkof string theory. In the theory including gravity, the duality naturally describes a gauge field livingon the hypersurface which inserts into a higher dimension space. However, in the past decades, thestudy of this duality has been extended and applied into many different domains, such as the strong-ly coupled dynamic of Quantum Color Dynamics and the electriweak theory, black hole physicsand quantum gravity, relativistic hyperdynamic and the application in condensed matter physics.In the application of Anti-de-Sitter/Condensed matter theory(AdS/CMT), people has constructedcolorful holographic superconductor or superfluid model and holographic (non)-relativistic (non)-fermi system. Also, AdS/CMT correspondence has been well applied in the study of physicalphenomena, for example, quantum critical points, strange metal, quantum Hall effect and spindensity wave and so on. Many remarkable progresses have been made in these fields.Based on the background above, in this thesis, we will use the powerful AdS/CFT dualityto investigate the physical features in kinds of strongly coupled systems. After the brief reviewon the AdS/CFT duality theory and the concrete dictionary dual to condensed matter physics, theremaining contents of this thesis mainly focus on the construction of the AdS/CMT model andthen exploring their various physical features.In chapter2, as a first step, we introduce the higher derivative coupling between the U (1)gauge field and the scalar field. Firstly, we construct the holographic superconductor in probe limit.Through analytical and numerical method, our conclusion without the magnetic field is that thestronger coupling will make the condensation easier to form. When the external magnetic field isconsidered, we investigate the dependence of the critical temperature on the critical magnetic fieldand find the reminiscent of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state. Secondly, we explorethe holographic superconductor with full backreaction. we holographically describe the proximityeffect of the superconductor system by calculating its entanglement entropy and conductivity. Wetake the first step to describe this effect in the holographic framework.In chapter3, we firstly explore the first and second order phase transition and their characters.We conclude that conductivity and pair susceptibility can be considered as the probe to distinguish the two kinds of phase transitions. Then, we extend the discussion into AdS soliton, we find thefirst order phase transition do not appear in this case. we also observe that the behavior of its pairsusceptibility is, in some degree, similar to the instability of BCS pair.In the following chapter4and5, we investigate the existence of Fermi surface and variousfeatures of the spectral function in holographic Fermi system.We consider the holographic fermions in the Gauss-Bonnet AdS background in chapter4.We show that in addition to the strength of the dipole coupling, the spacetime dimension and thehigher curvature correction in the gravity background also influence the onset of the Fermi gap andthe gap distance. We see that there are richer physics in the boundary fermion system due to themodification in the bulk gravity.In chapter5, We study the holographic non-relativistic fermions in the presence of the bulkdipole coupling in a charged dilatonic black hole background. We find that the presence of theflat band in the non-relativistic case will suppress the Fermi momentum. We also observe that theeffect of the dipole coupling in the dilaton gravity is more explicit. Finally, we observe that a phasetransition from an insulator to a conducting state as the fermion system becomes hotter.