Thermal and quantum phase transitions in a holographic anisotropic Dirac semimetal

In this thesis we build a phenomenological, strongly coupled quantum field theory in $2+1$-dimensions through AdS/CFT holography, by building a $3+1$-dimensional, negatively curved gravity theory with a $SU(2)$ gauge field, and a scalar field in the adjoint of $SU(2)$. We locate a phase transition between two distinct phases at zero and finite temperature, which are characterized through the dispersion relation of quasi-normal modes of probe fermions in the bulk, and correspond either to a Dirac semimetal or a band insulator. These phases are separated by a critical phase/critical point (depending if $T>0$ or $T=0$, respectively) where the band structure of boundary fermions exhibits semi-Dirac anisotropy. We characterize each phase at $T=0$ by explicit solutions to the bulk equations of motion in the infra-red, and determine that the critical point's spacetime is a Lifshitz geometry, whose dynamical critical exponent is approximately equal to $2$. We also find that this anisotropy induces a non-trivial scaling of the shear viscosity-entropy density ratio with respect to temperature in the $T\to 0$ limit, and find evidence that the anisotropic phase of the system corresponds to a finite-temperature quantum critical phase.