Relevant Degree Programs
Graduate Student Supervision
Doctoral Student Supervision (Jan 2008 - May 2021)
Many interesting phenomena, such as high-temperature superconductivity and the quark-gluon plasma, still lack a satisfyingly predictive theoretical description. However, recent advances have revealed a curious connection between quantum field theories at strong coupling and classical gravity. This correspondence, known as the gauge/gravity duality or holographic correspondence, offers a promising perspective for investigating strongly correlated systems. In this thesis, we focus on using these new tools to examine the consequences of breaking translational invariance in such systems.We first use this duality to study the holographic realization of a spatially inhomogeneous condensed matter device known as a Josephson junction. We do so by constructing the gravitational equivalent of two superconductors separated by a weak metallic link, from which we then extract various field-theoretic quantities of interest. These include the spontaneously generated Josephson current, the superconducting order parameter, as well as a novel quantity we refer to as edge currents, which are indicative of gapless chiral modes localized at the interfaces between phases.We then investigate the more abstract construct of entanglement entropy in holographic theories. We model the fast local injection of energy in a 2+1 dimensional field theory and study the resulting thermalization of quantum entanglement. We achieve this objective by numerically evolving the geometry dual to a local quench from which we then compute the area of various minimal surfaces, the holographic proxy for entanglement entropy. We observe the appearance of a lightcone featuring two distinct regimes of entanglement propagation and provide a phenomenological explanation of the underlying mechanisms at play.Finally, we turn our attention to spatial inhomogeneities in gravitational systems themselves. We use an approximation of general relativity in which the number of spacetime dimensions is infinite to investigate the Gregory-Laflamme instability of higher-dimensional charged black branes. We argue that charged branes are always unstable in this new language, and push the approximation to next-to-leading order to compute the critical dimension below which the instability results in horizon fragmentation. We also examine the stability properties of two-dimensional black membranes and find that the triangular lattice minimizes brane enthalpy.
This thesis studies strongly coupled phases of condensed matter physics using a combination of gauge-gravity correspondence and numerical methods. We examine holographic models of the condensed matter phenomena of: vortex formation in the spontaneously broken phase of gauge theories, spontaneous breaking of translational invariance by periodic modulation, properties of (non-)Fermi liquids, and metal-insulator transitions in systems with sourced periodic modulation.In Chapter 2, we formulate a criterion for the existence of a Higgs phase based on the existence of bulk solitons. This criteria is applicable when the microscopic details of the gauge theory are unknown. We demonstrate the existence of such solitons in both top-down and bottom-up examples of holographic theories and examine their thermodynamics.In Chapter 3, we construct inhomogeneous, asymptotically Anti-deSitter Space (ADS) black hole solutions in Einstein-Maxwell-axion theory corresponding to the spontaneous breaking of translational invariance and the formation of striped order in the dual 2 + 1 dimensional Quantum Field Theory (QFT). We investigate the phase structure as function of parameters.In Chapter 4, we continue the study begun in Chapter 3. On domains of both fixed and variable wavenumber, we find a second order phase transition to the striped solution in each of the grand canonical, canonical and microcanonical ensembles. We also examine the properties of the bulk black hole solutions.In Chapter 5, we consider a phenomenological model whose bosonic sector is governed by the DBI action, and whose charged sector is purely fermionic. In this model, we demonstrate the existence of a compact worldvolume embedding, stabilized by a Fermi surface on a D-brane. We study the bulk and dual QFT thermodynamic and transport properties.In Chapter 6, we analyze low energy thermo-electric transport in a class ofbottom-up, holographic models in which translation invariance has been broken. As a function of our choice of couplings, which parameterize this class of theories, we obtain (i) coherent metallic, or (ii) insulating, or (iii) incoherent metallic phases. We use a combination of analytical and numerical techniques to study the Alternating Current (AC) and Direct Current (DC) transport properties of these phases.
The AdS/CFT correspondence, which connects a d-dimensional field theory to a (d+1)-dimensional gravity, provides us with a new method to understand and explore physics. One of its recent interesting applications is holographic condensed matter theory. We investigate some holographic superconductivity models and discuss their properties. Both Abelian and non-Abelian models are studied, and we argue the p-wave solution is a hard-gapped superconductor. In a holographic system containing Fermions, the properties of a non-Fermi liquid with a Fermi surface are found. Weshow that a Landau level structure exists when external magnetic field is turned on, and argue for the existence of Fermi liquid when using the global coordinate system of AdS. Finite temperature results of the Fermion system are also given. In addition, a gravitational instability interpreted as a bubble of nothing is described, together with its field theory dual.
Master's Student Supervision (2010 - 2020)
There has been renewed interest in understanding the details and origins of chaos in quantum systems with many degrees of freedom. Chaos plays a significant role in holographic theories, hydrodynamic transport, and even the strange metal phase of condensed matter systems. With this importance, discovering a unified origin that yields universal results for chaotic systems is clearly desirable.In this thesis, we investigate the conjectured hydrodynamic origin of quantum many-body chaos, first posited in , by testing it with the next-to-leading order SYK model. We provide a review of how hydrodynamic theories are constructed, and how hydrodynamic theories with a certain symmetry possess all the standard features of chaos. We then review the leading order SYK model, demonstrate its chaotic behaviour, and compare it with the predictions of the hydrodynamic theory. We finally perform an in-depth investigation of the next-to-leading order SYK model, demonstrating that, while one sector of the theory satisfies the conjecture, another sector does not admit a hydrodynamic description. This shows that the conjecture must be modified to account for near-maximally chaotic theories.
Topological insulators are materials that are insulating in the bulk but conductive on the boundary. Although standard condensed matter techniques elucidate the dissipationless boundary physics of topological insulators well at weak coupling, they fail to do the same at strong coupling where exciting phenomena such as emergence and fractionalization are likely to occur. Fortunately the AdS/CFT correspondence offers an alternative perspective of the strong coupling limit in the form of a classical supergravity dual. In this thesis we realize the interface of a strongly-interacting fractional (2+1)D time-reversal invariant topological insulator at finite temperature by embedding a D5-brane with a $U(1)$ chemical potential into (AdS₅ black hole) × S⁵ supergravity. The thermodynamics of our interface are found to be considerably fermionic. Study of the interface has promising applications ranging from the design of spin channels in quantum computing, to the deeper understanding of highly-entangled systems.
A gravitational dual description to the Chiral Gross-Neveu model with infinite number of fermion fields is examined at finite fermion density. Under a number of simplifying assumptions, it is determined qualitatively that above a critical density, chiral symmetry is restored. The QFT side is reviewed as well. Using a method that does not require a limit from finite temperature situation, nor bosonization techniques, it is shown that, on the QFT side, symmetry is restored above a critical value of the chemical potential.