Weakly Correlated Studies of Strongly Correlated Systems
In this dissertation we employ and develop several different methods for studying strongly correlated electronic physics with the goal of realizing exotic quantum phenomena. In the first half, we use the density matrix renormalization group (DMRG) to probe the superconducting tendencies of a variety of strongly correlated systems. We start by investigating the triangular lattice Hubbard model as motivated by the organic salts, cobaltates, and recent Moir\'e superlattice materials. Here we find a clear transition from $p$-wave superconductivity at moderate on-site repulsion to $d$-wave superconductivity at strong on-site repulsion. Given the unusual tunability that Moir\'e superlattices offer in controlling the relative interaction strength, $U/t$, we thus provide a potential route for realizing a transition between $d$-wave and $p$-wave superconductivity via interlayer twist angles. We subsequently modify this model to mimic the band structure of the hole-doped transition metal dichalcogenides and establish evidence for spatially modulated superconductivity i.e. pair density wave ordering. Together, these works suggest that the interplay of frustration and moderately repulsive electronic interactions can be used to drive unconventional superconductivity. The latter half of this work is largely a product of the growing synergy between the physics and machine learning communities. We first use supervised machine learning to identify quantum phase transitions in a disordered, transverse field Ising model with Ising-duality preserving interactions. Specifically, we use a neural network trained on entanglement spectra to identify non-equilibrium, thermal-MBL phase transitions in this model and show that our method outperforms traditional regression schemes. Our approach has several additional advantages in that it offers a single framework for identifying multiple types of order, can enable a speedy exploration of large phase spaces by providing meaningful information from single disorder configurations, and has the potential to identify previously unknown phases. We go on to use unsupervised machine learning in order to identify quantum phase transitions in large volume, experimental single crystal x-ray diffraction data. In this setting, data analysis is becoming an increasingly prominent bottleneck with advancements in detector capabilities for X-ray and neutron scattering enabling researchers to collect hundreds of GB to several TB of data in the span of a few hours. To address this, we present a novel label-diffused Gaussian mixture model for clustering over temperature dependences of scattering intensities that allows us to readily identify phase transitions. Our algorithm is capable of analyzing hundreds of GBs of data in the span of minutes, offering the tantalizing possibility of real time analysis. Applications to several materials are discussed.
Nowack, Katja C.; Ginsparg, Paul
Ph. D., Physics
Doctor of Philosophy
dissertation or thesis