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Novel Quantum Monte Carlo Approaches for Quantum Liquids
Quantum Monte Carlo methods are a powerful suite of techniques for solving the quantum many-body problem. By using random numbers to stochastically sample quantum properties, QMC methods are capable of studying low-temperature quantum systems well beyond the reach of conventional deterministic techniques. QMC techniques have likewise been indispensible tools for augmenting our current knowledge of superfluidity and superconductivity. In this thesis, I present two new quantum Monte Carlo techniques, the Monte Carlo Power Method and Bose-Fermi Auxiliary-Field Quantum Monte Carlo, and apply previously developed Path Integral Monte Carlo methods to explore two new phases of quantum hard spheres and hydrogen. I lay the foundation for a subsequent description of my research by first reviewing the physics of quantum liquids in Chapter One and the mathematics behind Quantum Monte Carlo algorithms in Chapter Two. I then discuss the Monte Carlo Power Method, a stochastic way of computing the first several extremal eigenvalues of a matrix too memory-intensive to be stored and therefore diagonalized. As an illustration of the technique, I demonstrate how it can be used to determine the second eigenvalues of the transition matrices of several popular Monte Carlo algorithms. This information may be used to quantify how rapidly a Monte Carlo algorithm is converging to the equilibrium probability distribution it is sampling. I next present the Bose-Fermi Auxiliary-Field Quantum Monte Carlo algorithm. This algorithm generalizes the well-known Auxiliary-Field Quantum Monte Carlo algorithm for fermions to bosons and Bose-Fermi mixtures. Despite some shortcomings, the Bose-Fermi Auxiliary-Field Quantum Monte Carlo algorithm represents the first exact technique capable of studying Bose-Fermi mixtures of any size in any dimension. In Chapter Six, I describe a new Constant Stress Path Integral Monte Carlo algorithm for the study of quantum mechanical systems under high pressures. While the eventual hope is to apply this algorithm to the exploration of yet unidentified high-pressure, low-temperature phases of hydrogen, I employ this algorithm to determine whether or not quantum hard spheres can form a low-temperature bcc solid if exchange is not taken into account. In the final chapter of this thesis, I use Path Integral Monte Carlo once again to explore whether glassy para-hydrogen exhibits superfluidity. Physicists have long searched for ways to coax hydrogen into becoming a superfluid. I present evidence that, while glassy hydrogen does not crystallize at the temperatures at which hydrogen might become a superfluid, it nevertheless does not exhibit superfluidity. This is because the average binding energy per p-H2 molecule poses a severe barrier to exchange regardless of whether the system is crystalline. All in all, this work extends the reach of Quantum Monte Carlo methods to new systems and brings the power of existing methods to bear on new problems
A first-principles study of bilayer 1T'-WTe2/CrI3: A candidate topological spin filter
The ability to manipulate electronic spin channels in 2D materials is crucial
for realizing next-generation spintronics. Spin filters are spintronic
components that polarize spins using external electromagnetic fields or
intrinsic material properties like magnetism. Recently, topological protection
from backscattering has emerged as an enticing feature through which the
robustness of 2D spin filters might be enhanced. In this work, we propose and
then characterize one of the first 2D topological spin filters: bilayer
CrI3/1T'-WTe2. To do so, we use a combination of Density Functional Theory and
maximally localized Wannier functions to demonstrate that the bilayer (BL)
satisfies the principal criteria for being a topological spin filter; namely
that it is gapless, exhibits charge transfer from WTe2 to CrI3 that renders the
BL metallic despite the CrI3 retaining its monolayer ferromagnetism, and does
not retain the topological character of monolayer 1T'-WTe2. In particular, we
observe that the atomic magnetic moments on Cr from DFT are approximately 3.2
mB/Cr in the BL compared to 2.9 mB/Cr with small negative ferromagnetic (FM)
moments induced on the W atoms in freestanding monolayer CrI3. Subtracting the
charge and spin densities of the constituent monolayers from those of the BL
further reveals spin-polarized charge transfer from WTe2 to CrI3. We find that
the BL is topologically trivial by showing that its Chern number is zero.
Altogether, this evidence indicates that BL 1T'-WTe2/CrI3 is gapless, magnetic,
and topologically trivial, meaning that a terraced WTe2/CrI3 BL heterostructure
in which only a portion of a WTe2 monolayer is topped with CrI3 is a promising
candidate for a 2D topological spin filter. Our results further suggest that 1D
chiral edge states may be realized by stacking strongly hybridized FM
monolayers, like CrI3, atop 2D nonmagnetic Weyl semimetals like 1T'-WTe2
Finite-temperature auxiliary-field quantum Monte Carlo technique for Bose-Fermi mixtures
We present a quantum Monte Carlo (QMC) technique for calculating the exact finite-temperature properties of Bose-Fermi mixtures. The Bose-Fermi auxiliary-field quantum Monte Carlo (BFAFQMC) algorithm combines two methods, a finite-temperature AFQMC algorithm for bosons and a variant of the standard AFQMC algorithm for fermions, into one algorithm for mixtures. We demonstrate the accuracy of our method by comparing its results for the Bose-Hubbard and Bose-Fermi-Hubbard models against those produced using exact diagonalization for small systems. Comparisons are also made with mean-field theory and the worm algorithm for larger systems. As is the case with most fermion Hamiltonians, a sign or phase problem is present in the BFAFQMC algorithm. We discuss the nature of these problems in this framework and describe how they can be controlled with well-studied approximations to expand the BFAFQMC algorithm\u27s reach. This algorithm can serve as an essential tool for answering many unresolved questions about many-body physics in mixed Bose-Fermi systems