Towards exact numerical solutions of quantum many-body problems in ultracold Bose gases : a dissertation presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Physics at Massey University, Albany, New Zealand
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Date
2022
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Massey University
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Abstract
The main objective of this thesis is to examine how the full configuration interaction quantum Monte Carlo (FCIQMC) method can be best utilized for studying ultracold Bose gases. FCIQMC is a stochastic approach for finding the ground state of a quantum many-body Hamiltonian. It is based on the dynamical evolution of a walker population in Hilbert space, which samples the ground state configuration vector over many iterations. The method has been previously applied to studies of the electronic structure of molecules, solids and certain spin models, as well as recently to ultracold Fermi gases. Whereas in this work we are interested in using the method to examine ultracold bosonic atoms. In this thesis, we cover methodological developments and applications of the FCIQMC method. Two main themes are covered in this thesis: methodological developments and applications of the full configuration interaction quantum Monte Carlo method. Firstly, we present a modification of the original protocol in FCIQMC for walker population control of Booth et al. [J. Chem. Phys. 131, 054106 (2009)] in order to achieve equilibration at a pre-defined average walker number and to avoid walker number overshoots. Next, we investigate a systematic statistical bias found in FCIQMC, known as the population control bias, that originates from controlling a walker population with a fluctuating shift parameter and can become large in bosonic systems. We use an exactly solvable stochastic differential equation to model the bias. Lastly, we showcase an application of FCIQMC in studying the properties of the lowest-energy momentum eigenstates, known as yrast states, of Bose gases coupled with a mobile impurity in one spatial dimension. Based on the results of our computations, we identify different dynamical regimes: the polaron and depleton regimes and transitions between them.
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Listed in 2022 Dean's List of Exceptional Theses
Keywords
Bosons, Bose-Einstein gas, Cold gases, Mathematics, Monte Carlo method, Dean's List of Exceptional Theses