First-principles Deep Learning for Quantum Many-body Physics

Abstract

This thesis investigates emergent phenomena in strongly correlated quantum matter, with a central focus on developing first-principles deep learning methods for quantum many-body systems. A common theme throughout this work is the search for microscopic mechanisms that generate unexpected collective behavior, together with computational frameworks capable of describing such behavior in regimes where conventional approaches become inadequate. The first part of the thesis studies a doped Mott insulator in a magnetic field and uncovers a new superconducting state, which we call \emph{magnonic superconductivity}. In this state, magnons mediate pairing, and the superconducting order is carried by composite objects binding electron pairs to spin excitations. This mechanism gives rise to a partially spin-polarized superconducting phase beyond the conventional paradigm of electron pairing and further suggests the possibility of higher-charge bound states, including charge-$6e$ superconductivity. The main thrust of the thesis is the use of deep neural networks as variational, first-principles representations of many-body wave functions. In contrast to the usual data-driven role of machine learning, the neural-network ans\"atze developed here do not learn from labeled datasets; instead, they are optimized directly from the microscopic Hamiltonian through variational Monte Carlo. Within this framework, we first develop self-attention-based neural-network wave functions for correlated electrons in solids and show that they accurately describe moir\'e systems with minimal human bias, capture interaction-driven phase transitions, and exhibit favorable scaling of representational complexity with system size. We then introduce a general physics-informed initialization strategy that reconstructs complex many-body wave functions from probability density and probability current. This approach enables highly accurate pretraining of neural wave functions, achieves near-exact overlaps for topological and paired quantum states, and allows efficient simulations of fractional quantum Hall systems with realistic interactions at unprecedented sizes. Finally, we introduce QERNEL, an efficient foundational neural variational ansatz designed to learn a family of many-body ground states within a single conditional model. By combining efficient context conditioning with modern permutation-equivariant building blocks, QERNEL achieves substantially improved expressivity at low computational cost. Applied to interacting electrons in semiconductor moir\'e heterobilayers, it captures distinct many-body phases and resolves the sharp phase transition between them in systems as large as 150 electrons. These results show that context-aware neural wave functions can move beyond Hamiltonian-by-Hamiltonian solution toward genuinely foundational models of quantum matter. Taken together, the results of this thesis show that first-principles deep learning can serve not merely as a numerical tool, but as a general framework for quantum many-body physics: one that bridges microscopic Hamiltonians, expressive wave-function ansätze, and scalable computation, while opening new paths to the discovery and characterization of strongly correlated quantum matter.