Doctor of Philosophy, The Ohio State University, 2024, Physics

Phase transitions occur in many classical and quantum systems, and are the subject of many an open problem in physics. In the past decade, the conformal bootstrap has provided new perspectives for looking at the critical point of a transition. With this formalism, it is possible to exploit the conformal symmetry intrinsically present at the critical point, and derive general results about classes of transitions that obey the same symmetries. This thesis presents the application of this method to two problems of note in classical and quantum phase transitions. The first is a classical model of O(N) spins in the presence of a boundary. We use the numerical conformal bootstrap to prove rigorously the existence of a new boundary phase in three-dimensional Heisenberg (O(3)) and O(4) magnets, deemed the extraordinary-log universality class. The results agree well with a parallel numerical study but are more rigorous due to the bounded nature of the error. The second case is the inherently quantum problem of Anderson transitions between metals and insulators. It has been discovered that at criticality, the wavefunctions describe multifractal objects, that are described by infinitely many fractal dimensions. We use analytical constraints from conformal symmetry to predict the form of these fractal parameters in dimensions greater than two. Our exact prediction, which works in arbitrary dimensions, can be used as a probe for conformal symmetry at Anderson transitions. By studying these two problems, we demonstrate the power of conformal symmetry as a non-perturbative tool in the theory of phase transitions in arbitrary dimensions. Throughout the thesis, we have extended the domain of applicability of traditional bootstrap techniques for the purpose of non-unitary and non-positive systems.

Committee: Ilya Gruzberg (Advisor); Marc Bockrath (Committee Member); Samir Mathur (Committee Member); Yuanming Lu (Committee Member) Subjects: Condensed Matter Physics; Physics

Doctor of Philosophy, The Ohio State University, 2019, Physics

Superconductivity has been at the heart of research into quantum phenomena since its discovery over a century ago. More recently efforts have been made to understand the nature of the quantum phase transition (QPT) that separates the superconducting and insulating phases in certain 2D materials at zero temperature. This superconductor-insulator transition (SIT) has been theoretically and experimentally proven to be driven by quantum fluctuations of the superconducting phase instead of the breakup of Cooper pairs. In this thesis we present a study of quantum fluctuations across the SIT and how they can be imaged in both theoretical simulations and experimental measurements. We begin with an overview of the field from a historical perspective, describing the development of the theory of SITs driven by experiments on thin films. We present the Josephson junction array (JJA) model as a paradigm to investigate the quantum phase fluctuation-driven SIT using quantum Monte Carlo (QMC) techniques. We explore the manifestation of quantum fluctuations across the SIT in three different local measurements: the diamagnetic susceptibility χ(r), two-particle density of states P(r, ω), and compressibility κ(r), revealed through their local maps and calculated via QMC. χ(r) probes the system's ability to generate diamagnetic currents and its local map displays growing fluctuations upon increasing both temperature the quantum tuning parameter g. Remarkably, however, these fluctuations persist well below Tc as the SIT is approached, indicating the quantum nature of these fluctuations. We compare our results to SQUID susceptometry measurements performed on thin-film NbTiN and find good qualitative agreement. The map of κ(r) paints a similar picture when tuned via g, but in contrast to χ(r), we find a fundamental difference in its evolution with temperature, providing a complementary local probe to χ(r). P(r, ω), obtained using Maximum Entropy analytic continuation of imaginary time Q (open full item for complete abstract)

Committee: Nandini Trivedi (Advisor); Yuan-Ming Lu (Committee Member); Rolando Valdes-Aguilar (Committee Member); Richard Furnstahl (Committee Member) Subjects: Physics; Theoretical Physics

Doctor of Philosophy, The Ohio State University, 2014, Physics

This dissertation documents the conception, development, validation, and application of an inductive experimental measurement of the critical Cooper pair momentum in thin superconducting films. A current-carrying (drive) coil of radius much smaller than the film radius induces a highly inhomogeneous screening supercurrent density in the film. The magnitude of the supercurrent is greatest at a radial position corresponding to the coil radius. It is shown that subject to magnetic fields greater than a few mG, the film is in a metastable superconducting state with respect to the formation of flux-bearing vortex-antivortex excitations. Consequently, magnetic coupling to a second (pickup) coil located co-axially on the opposite side of the film is independent of the drive coil current (linear response). As the drive coil current is increased and the highest-momentum Cooper pairs approach a momentum sufficient to break the pairs, the free-energy barrier to vortex-antivortex pair creation is diminished and such pairs appear en masse, detected as a crossover to nonlinear coupling between the coils. A scheme for calculating this critical momentum from the corresponding drive coil field is presented with the empirical assumption that the peak out-of-phase coil coupling corresponds to the upper limit of Meissner state metastability. This assumption is validated by independent measurements of the critical pair momentum and upper critical magnetic field performed on film samples of niobium and ii molybdenum-germanium alloy. These measurements are connected through the phenomenological superconducting coherence length, and the data show quantitative agreement in these well-studied superconductors. A second experimental study is presented for a collection of cuprate films of varied doping. It is seen that the critical momentum scales roughly with the measured transition temperature, as predicted by a universal model of cuprate superconductivity.

Committee: Thomas Lemberger Ph.D. (Advisor); Fengyuan Yang Ph.D. (Committee Member); Mohid Randeria Ph.D. (Committee Member); Richard Hughes Ph.D. (Committee Member); Xiaodong Sun Ph.D. (Other) Subjects: Condensed Matter Physics; Physics