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Numerical holographic condensed matter Smyth, Darren

Abstract

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 of bottom-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.

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Attribution-NonCommercial-NoDerivs 2.5 Canada

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