Physics Commons^™

Partial Muon Capture Rates In A = 3 And A = 6 Nuclei With Chiral Effective Field Theory, G. B. King, S. Pastore, M. Piarulli, Rocco Schiavilla

Physics Faculty Publications

Searches for neutrinoless double-β decay rates are crucial in addressing questions within fundamental symmetries and neutrino physics. The rates of these decays depend not only on unknown parameters associated with neutrinos, but also on nuclear properties. In order to reliably extract information about the neutrino, one needs an accurate treatment of the complex many-body dynamics of the nucleus. Neutrinoless double-β decays take place at momentum transfers on the order of 100MeV /c and require both nuclear electroweak vector and axial current matrix elements. Muon capture, a process in the same momentum transfer regime, has readily available experimental data to validate …

Quantum Phases And Phase Transitions In Designer Spin Models, Nisheeta Desai

Theses and Dissertations--Physics and Astronomy

This work focuses on numerical studies of quantum spin systems. These simple models are known to exhibit a variety of phases, some of which have no classical counterpart. Phase transitions between them are driven by quantum fluctuations and the unconventional nature of some such transitions make them a fascinating avenue of study.

Quantum Monte Carlo (QMC) is an indispensable tool in the study of these phases and phase transitions in two and higher dimensions. Nevertheless, we are limited by our inability to simulate models that suffer from the infamous sign problem. While the case of S=1/2 has been studied …

Unsupervised Machine Learning Account Of Magnetic Transitions In The Hubbard Model, Kelvin Ch'ng, Nick Vazquez, Ehsan Khatami

Faculty Publications

We employ several unsupervised machine learning techniques, including autoencoders, random trees embedding, and t-distributed stochastic neighboring ensemble (t-SNE), to reduce the dimensionality of, and therefore classify, raw (auxiliary) spin configurations generated, through Monte Carlo simulations of small clusters, for the Ising and Fermi-Hubbard models at finite temperatures. Results from a convolutional autoencoder for the three-dimensional Ising model can be shown to produce the magnetization and the susceptibility as a function of temperature with a high degree of accuracy. Quantum fluctuations distort this picture and prevent us from making such connections between the output of the autoencoder and …

Understanding Three-Body Interactions In Hexagonal Close Packed Solid He-4, Ashleigh Locke Barnes

Doctoral Dissertations

The ground state properties of hexagonal close packed (hcp) solid ⁴He [He-4] are dominated by large atomic zero point motions which make the primary contribution to the solid’s low-temperature Debye-Waller (DW) factors. Preliminary investigations have also suggested that three-body interactions can play an important role in this system, particularly at higher densities. However, due to their computational cost, these interactions are not generally incorporated into theoretical models of solid ⁴He [He-4]. In order to accurately treat both zero point motion and three-body interactions, we have developed a perturbative treatment in which the three-body energy is added as a …

Deconfined Quantum Criticality In 2d Su(N) Magnets With Anisotropy, Jonathan D'Emidio

Theses and Dissertations--Physics and Astronomy

In this thesis I will outline various quantum phase transitions in 2D models of magnets that are amenable to simulation with quantum Monte Carlo techniques. The key player in this work is the theory of deconfined criticality, which generically allows for zero temperature quantum phase transitions between phases that break distinct global symmetries. I will describe models with different symmetries including SU(N), SO(N), and "easy-plane" SU(N) and I will demonstrate how the presence or absence of continuous transitions in these models fits together with the theory of deconfined criticality.

Sign-Problem-Free Monte Carlo Simulation Of Certain Frustrated Quantum Magnets, Fabien Alet, Kedar Damle, Sumiran Pujari

Physics and Astronomy Faculty Publications

We introduce a quantum Monte Carlo (QMC) method for efficient sign-problem-free simulations of a broad class of frustrated S =1/2 antiferromagnets using the basis of spin eigenstates of clusters to avoid the severe sign problem faced by other QMC methods. We demonstrate the utility of the method in several cases with competing exchange interactions and flag important limitations as well as possible extensions of the method.

Hard-Wall And Non-Uniform Lattice Monte Carlo Approaches To One-Dimensional Fermi Gases In A Harmonic Trap, Casey E. Berger, Joaquín E. Drut, William J. Porter

Physics: Faculty Publications

We present in detail two variants of the lattice Monte Carlo method aimed at tackling systems in external trapping potentials: a uniform-lattice approach with hard-wall boundary conditions, and a non-uniform Gauss–Hermite lattice approach. Using those two methods, we compute the ground-state energy and spatial density profile for systems of N=4–8 harmonically trapped fermions in one dimension. From the favorable comparison of both energies and density profiles (particularly in regions of low density), we conclude that the trapping potential is properly resolved by the hard-wall basis. Our work paves the way to higher dimensions and finite temperature analyses, as calculations with …

Interaction-Induced Dirac Fermions From Quadratic Band Touching In Bilayer Graphene, Sumiran Pujari, Thomas C. Lang, Ganpathy Murthy, Ribhu K. Kaul

Physics and Astronomy Faculty Publications

We revisit the effect of local interactions on the quadratic band touching (QBT) of the Bernal honeycomb bilayer model using renormalization group (RG) arguments and quantum Monte Carlo (QMC) simulations. We present a RG argument which predicts, contrary to previous studies, that weak interactions do not flow to strong coupling even if the free dispersion has a QBT. Instead, they generate a linear term in the dispersion, which causes the interactions to flow back to weak coupling. Consistent with this RG scenario, in unbiased QMC simulations of the Hubbard model we find compelling evidence that antiferromagnetism turns on at a …

First-Order Superfluid To Valence-Bond Solid Phase Transitions In Easy-Plane Su(N) Magnets For Small N, Jonathan D'Emidio, Ribhu K. Kaul

Physics and Astronomy Faculty Publications

We consider the easy-plane limit of bipartite SU(N) Heisenberg Hamiltonians, which have a fundamental representation on one sublattice and the conjugate to fundamental on the other sublattice. For N = 2 the easy plane limit of the SU(2) Heisenberg model is the well-known quantum XY model of a lattice superfluid. We introduce a logical method to generalize the quantum XY model to arbitrary N, which keeps the Hamiltonian sign-free. We show that these quantum Hamiltonians have a world-line representation as the statistical mechanics of certain tightly packed loop models of N colors in which neighboring loops are …

Path Integral Quantum Monte Carlo Study Of Coupling And Proximity Effects In Superfluid Helium-4, Max Graves

Graduate College Dissertations and Theses

When bulk helium-4 is cooled below T = 2.18 K, it undergoes a phase transition to a superfluid, characterized by a complex wave function with a macroscopic phase and exhibits inviscid, quantized flow. The macroscopic phase coherence can be probed in a container filled with helium-4, by reducing one or more of its dimensions until they are smaller than the coherence length, the spatial distance over which order propagates. As this dimensional reduction occurs, enhanced thermal and quantum fluctuations push the transition to the superfluid state to lower temperatures. However, this trend can be countered via the proximity effect, where …

Population Size Bias In Descendant-Weighted Diffusion Quantum Monte Carlo Simulations, G. Lee Warren, Robert J. Hinde

Chemistry Publications and Other Works

We consider the influence of population size on the accuracy of diffusion quantum Monte Carlo simulations that employ descendant weighting or forward walking techniques to compute expectation values of observables that do not commute with the Hamiltonian. We show that for a simple model system, the d-dimensional isotropic harmonic oscillator, the population size must increase rapidly with d in order to ensure that the simulations produce accurate results. When the population size is too small, expectation values computed using descendant-weighted diffusion quantum Monte Carlo simulations exhibit significant systematic biases.

Population Size Bias In Descendant-Weighted Diffusion Quantum Monte Carlo Simulations, G. Lee Warren, Robert Hinde

Robert Hinde

We consider the influence of population size on the accuracy of diffusion quantum Monte Carlo simulations that employ descendant weighting or forward walking techniques to compute expectation values of observables that do not commute with the Hamiltonian. We show that for a simple model system, the d-dimensional isotropic harmonic oscillator, the population size must increase rapidly with d in order to ensure that the simulations produce accurate results. When the population size is too small, expectation values computed using descendant-weighted diffusion quantum Monte Carlo simulations exhibit significant systematic biases.

G. N. Lewis' Atom And Quantum Monte Carlo Studies Of Liquids, Randall W. Hall, Peter G. Wolynes

Randall W. Hall