Thèse de Juan Pablo Alvarez (LPT), Avril 2015

TITLE : Analytical and numerical study of the Superfluid - Bose glass transition in two dimensions

ABSTRACT : The interplay of disorder (i.e. impurities) and interactions is one of the most fundamental questions in Condensed Matter Physics that has received a lot attention in the past couple of decades. The quantum phase transition from Superfluid to Bose glass driven by disorder has puzzled theoreticians and experimentalists alike, leaving unresolved questions despite their best efforts. The work presented in this thesis addresses some of these questions for two models of disordered hard-core bosons in two dimensions. In particular, the values of the critical exponents governing the transition, the inhomogeneous properties of the competing phases, the physical scenario at criticality and the bosonic excitations’ localization properties are investigated. Three different approaches to the transition are used to explore this problem. We first show how Bose- condensate and superfluid fractions are affected by disorder in a Mean-Field approximation, which is unable to capture a transition, but reveals interesting qualitative features. Building on such a Mean-Field solution, quantum fluctuations are then introduced using a linear spin-wave theory in real space which does capture the transition and furthermore unveils a non-trivial behavior for the excitation spectrum. Finally, the quantum criticality is explored in great detail using state-of-the- art Quantum Monte Carlo simulations, leading to a precise evaluation of the critical exponents and a surprising absence of self-averaging in the Bose glass regime.

Keywords : Disorder, interactions, Bose glass, superfluid, hard-core bosons

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