Abstract:
The work in this thesis is concerned with the application and development of quantum
Monte Carlo (QMC) methods. We begin by proposing a technique to maximise the
efficiency of the extrapolation of DMC results to zero time step, finding that a relative
time step ratio of 1:4 is optimal.
We discuss the post-processing of QMC data and the calculation of accurate error bars
by reblocking, setting out criteria for the choice of block length. We then quantify the
effects of uncertainty in the correlation length on estimated error bars, finding that the
frequency of outliers is significantly increased for short runs.
We then report QMC calculations of biexciton binding energies in bilayer systems.
We have also calculated exciton-exciton interaction potentials, and radial distribution
functions for electrons and holes in bound biexcitons. We find a larger region of biexciton
stability than other recent work [C. Schindler and R. Zimmermann, Phys. Rev. B 78,
045313 (2008)]. We also find that individual excitons retain their identity in bound
biexcitons for large layer separations.
Finally, we give details of a QMC study of the one-dimensional homogeneous electron
gas (1D HEG). We present calculations of the energy, pair correlation function, static
structure factor (SSF), and momentum density (MD) for the 1D HEG. We observe peaks
in the SSF at even-integer-multiples of the Fermi wave vector, which grow as the coupling
is increased. Our MD results show an increase in the effective Fermi wave vector as the
interaction strength is raised in the paramagnetic harmonic wire; this appears to be a
result of the vanishing difference between the wave functions of the paramagnetic and
ferromagnetic systems. We have extracted the Luttinger liquid exponent from our MDs
by fitting to data around the Fermi wave vector, finding good agreement between the
exponents of the ferromagnetic infinitely-thin and harmonic wires.
