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|Title:||Non-equilibrium real time dynamics of quantum spin systems and the quantum critical dynamics of 'dirty' bosons|
|Authors:||Ng, Ray, Yeh Yi|
|Department:||Physics and Astronomy|
|Abstract:||This thesis presents our work on two separate subfields and has for this reason been divided into two parts: (I) the development and implementation of a numerical technique for non-equilibrium dynamics and a (II) detailed investigation of the dirty-boson problem. In part (I), we optimize and develop the quantum phase space method known as the positive-P representation (PPR) specifically for the simulations of the real time quench dynamics of quantum spin systems. The main benefit of this approach is that the dynamics of the density operator is mapped onto $\sim N$ stochastic variables (where $N$ is the size of the system) that obey Langevin-type stochastic differential equations, thereby greatly reducing the complexity of the problem. The first publication presents our initial use of the PPR on spin systems by using a Schwinger mapping for spin operators on to Bosonic operators since the underlying basis comprises of Bosonic coherent states. We simulate the quench dynamics of the generalized transverse-field spin-1/2 XXZ model in 1d showing that simulations of up to 100 spins are possible, albeit for relatively short simulation times. In our second publication, we reformulate the PPR using SU(2) spin coherent states and further optimize simulation lifetimes by implementing an extrapolation scheme, to achieve several-fold improvements over the results of our first publication. We focus solely on the transverse Ising model and simulate its quench dynamics in 1d and 2d using up to $10^4$ spins, while significantly extending simulation lifetimes. The second part of this thesis is a numerical study of the universality class of the Superfluid-Bose Glass transition of the dirty-boson system. Recently the longstanding exact result $z=d$, where $z$ is the dynamic critical exponent and $d$ is the dimensionality of the system, has been challenged by a series of numerical studies, suggesting the alternative scenario that $z$ should be instead unconstrained. To address this controversy, we use large scale quantum Monte-Carlo simulations on two independent quantum models, and average over $5\times10^4-10^5$ disorder realizations to numerically determine the universality class of the dirty-boson transition, paying particular attention to the dynamic critical exponent, $z$ and without any biasing assumptions.|
|Appears in Collections:||Open Access Dissertations and Theses|
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