MACHINE LEARNING AND MONTE CARLO STUDIES OF STRONGLY CORRELATED SYSTEMS
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One, if not the, major difficulty encountered in the theoretical study of many-bodyquantum systems is the exponential growth of the Hilbert space with increasing degrees of freedom. In strongly correlated systems, non-perturbative interaction effects can exacerbate this difficulty by preventing the mapping of the theory to a single-particle problem. A multitude of theoretical techniques have thus emerged with the goal of understanding and predicting the exotic behavior of strongly cor- related systems. Among them are Monte Carlo simulation and, more recently, machine learning. In this dissertation, we use and develop Monte Carlo and ma- chine learning methods with the aim of learning new physics in strongly correlated systems. In the first part we apply machine learning to data obtained from simulations of strongly correlated systems. The identification of phases and characterization of their universal properties is a ubiquitous aspect of research in condensed matter physics. One can view phase identification as a classification problem in which one uses some function to map data to a phase label. However, complications such as competing interactions, disorder, and topological order, can render commonly used functions such as local order parameters ineffective. Here, we use a supervised machine learning model to represent the function that maps data to a phase label. In particular we study the phase diagram of a disordered fractional quantum Hall system with competing interactions. In addition to this phase classification prob- lem, we also consider the question of whether a given quantum many-body wave function could even be the ground state of some local Hamiltonian. To this end we introduce Entanglement Clustering, which uses unsupervised machine learning to study unconverged, noisy Monte Carlo swap operator samples from wave functions. In the second part we apply machine learning to data obtained from exper- iments. One can view many experimental techniques as forward processes that take some experimental probe, let it interact with a sample, and produce an out- put dataset. The goal of the analysis of the output dataset is often to recover some information about the interaction of the probe with the sample such as an order parameter type or electrostatic potential. One way to do this is to attempt to find an inverse function that maps the dataset back to the desired information. Traditional solutions to such “inverse problems” often rely on the existence of a forward model. However, motivated by cases where there is no invertable and/or efficient forward model, we try instead to represent the inverse function as an ML model. With this guiding philosophy, we have been able to gain new insights into complex materials using data from resonant ultrasound spectroscopy experiments. In the third part, we approach the melting of generalized Wigner crystals by considering the strong coupling limit of a transition metal dichalcogenide (TMD) moiré system at varying densities using Monte Carlo simulations with a new cluster update algorithm. We are motivated by recent experiments in a narrow-band TMD heterobilayer moiré system that found signatures of incompressible charge ordered states at fractional fillings of the moiré lattice that one can understand as generalized Wigner crystals. We predict the generalized Wigner crystal at 1/3 filling to melt into the compressible hexagonal domain wall state upon increasing filling. Moreover, we find two distinct stripe solid states at fillings 2/5 and 1/2 to be each preceded by distinct types of nematic states.
Ramshaw, Brad Jared; Ginsparg, Paul
Ph. D., Physics
Doctor of Philosophy
dissertation or thesis