#### Date of Award

12-2015

#### Degree Type

Dissertation

#### Degree Name

Doctor of Philosophy

#### Major

Physics

#### Major Professor

George Siopsis

#### Committee Members

John J. Quinn, Norman Mannella, Fernando A. Schwartz

#### Abstract

We discuss a holographic model consisting of a *U(1)* gauge field and a scalar field coupled to a charged AdS (anti-de Sitter) black hole under a spatially homogeneous chemical potential. By turning on a higher-derivative interaction term between the *U(1)* gauge field and the scalar field, a spatially dependent profile of the scalar field is generated spontaneously. We calculate the critical temperature at which the transition to the inhomogeneous phase occurs for various values of the parameters of the system. We solve the equations of motion below the critical temperature, and show that the dual gauge theory on the boundary spontaneously develops a spatially inhomogeneous charge density. In addition to that we discuss the zeroes and poles of the determinant of the retarded Green function (det *G _{R}*) at zero frequency in a holographic system of charged massless fermions interacting via a dipole coupling. For large negative values of the dipole coupling constant

*p*, det

*G*possesses only poles pointing to a Fermi liquid phase. We show that a duality exists relating systems of opposite

_{R}*p*. This maps poles of det

*G*at large negative

_{R}*p*to zeroes of det

*G*at large positive

_{R}*p*, indicating that the latter corresponds to a Mott insulator phase. This duality suggests that the properties of a Mott insulator can be studied by mapping the system to a Fermi liquid and then for small values of

*p*, det

*G*contains both poles and zeroes (pseudo-gap phase). Finally, we study holographic fermions in the spontaneously generated holographic lattice background defined above. We solve the equations of motion below

_{R}*T*(critical temperature) and analyze the change in Fermi surface due to introduction of the holographic lattice. The band structure of this fermionic system was also analyzed numerically and it was found that a band gap was formed due to lattice effects.

_{c}#### Recommended Citation

Yeter Aydeniz, Kübra, "Spontaneously Generated Inhomogeneous Phases via Holography. " PhD diss., University of Tennessee, 2015.

https://trace.tennessee.edu/utk_graddiss/3621

#### Included in

Condensed Matter Physics Commons, Elementary Particles and Fields and String Theory Commons