Strongly correlated materials exhibit complex emergent phenomena -- such as unconventional high-temperature superconductivity -- that cannot be explained within a single or weakly-interacting particle description, making understanding their physics a central challenge in condensed matter physics. This thesis develops and applies novel approaches to strongly correlated electron systems, focusing on neural quantum states (NQS) and quantum simulation with cold atoms in optical lattices or Rydberg tweezer arrays. A key contribution of this work is the advancement of neural-network-based representations of quantum many-body states. By employing state-of-the-art network architectures like Transformers and combining them with physical constructions such as determinants, Pfaffians and Gutzwiller-projection, NQS are extended to simulate large two-dimensional fermionic single- and multi-band systems with high accuracy and beyond the capabilities of conventional methods. In addition, the thesis explores how quantum simulators based on ultracold atoms in optical lattices can be leveraged to study models directly relevant to strongly correlated materials -- e.g. the multi-band model of cuprate superconductors -- as well as proposes strategies to probe superconductivity in this setting. Furthermore, hybrid approaches that combine NQS with data from quantum simulators are developed. This synergy allows for improved optimization and direct comparison between theory and experiment. These methodological developments are applied to investigate two fundamental questions in high-temperature superconductivity: On the one hand, the work proposes a microscopic mechanism based on Feshbach resonances and tests this hypothesis extensively in a model system relevant to cuprates, nickelates and heavy fermion materials. On the other hand, it develops systematic approaches to derive effective low-energy models from more complex systems like multi-band models or electron-phonon coupled systems, shining light on the timely question which single-band models capture the physics of high-temperature superconductors like cuprate or nickelate materials. Overall, the thesis demonstrates how combining machine learning and quantum simulation provides powerful tools for understanding strongly correlated quantum matter.
Strongly correlated materials exhibit complex emergent phenomena -- such as unconventional high-temperature superconductivity -- that cannot be explained within a single or weakly-interacting particle description, making understanding their physics a central challenge in condensed matter physics. This thesis develops and applies novel approaches to strongly correlated electron systems, focusing on neural quantum states (NQS) and quantum simulation with cold atoms in optical lattices or Rydberg tweezer arrays. A key contribution of this work is the advancement of neural-network-based representations of quantum many-body states. By employing state-of-the-art network architectures like Transformers and combining them with physical constructions such as determinants, Pfaffians and Gutzwiller-projection, NQS are extended to simulate large two-dimensional fermionic single- and multi-band systems with high accuracy and beyond the capabilities of conventional methods. In addition, the thesis explores how quantum simulators based on ultracold atoms in optical lattices can be leveraged to study models directly relevant to strongly correlated materials -- e.g. the multi-band model of cuprate superconductors -- as well as proposes strategies to probe superconductivity in this setting. Furthermore, hybrid approaches that combine NQS with data from quantum simulators are developed. This synergy allows for improved optimization and direct comparison between theory and experiment. These methodological developments are applied to investigate two fundamental questions in high-temperature superconductivity: On the one hand, the work proposes a microscopic mechanism based on Feshbach resonances and tests this hypothesis extensively in a model system relevant to cuprates, nickelates and heavy fermion materials. On the other hand, it develops systematic approaches to derive effective low-energy models from more complex systems like multi-band models or electron-phonon coupled systems, shining light on the timely question which single-band models capture the physics of high-temperature superconductors like cuprate or nickelate materials. Overall, the thesis demonstrates how combining machine learning and quantum simulation provides powerful tools for understanding strongly correlated quantum matter.
The study of strongly correlated materials remains one of the most challenging and active frontiers in condensed matter physics. In these systems, the intricate interplay between electrons' kinetic energy and their mutual Coulomb repulsion gives rise to a plethora of exotic phenomena, from high-temperature superconductivity to giant magnetoresistance, which cannot be explained by conventional one-electron theories. This necessitates the development and application of advanced theoretical and computational methods capable of capturing the essential physics of strong electronic correlations. A diverse array of numerical and analytical techniques has been developed to tackle the many-body problem. However, no single method serves as a panacea; each comes with its own set of strengths and weaknesses, and their domains of applicability vary significantly. The choice of an appropriate approximation is therefore highly dependent on the specific physical system and the scientific question at hand. Different problems may benefit from different, and sometimes complementary, methodological perspectives. This thesis focuses primarily on the application and development of local or quasi-local approaches. The rationale for this focus is rooted in the physical reality of many key correlated materials, such as transition metal oxides, heavy-fermion systems or molecular solids like alkali-doped fullerenes, where the local on-site electronic interaction is the dominant energy scale. By prioritizing the accurate treatment of local physics, these methods provide a robust and computationally efficient approximation for understanding a wide range of material properties. Recent experimental and theoretical advancements—spanning the rich physics of multiorbital compounds, the precise control over interactions in ultracold atomic gases, and the complex interplay in electron-phonon coupled systems—have created an urgent need for theoretical frameworks that can deliver reliable and rapid insights. The methods explored in this work are meant to address these challenges, offering a balance between accuracy and computational feasibility. Given the variety of topics addressed, from methodological developments to their application in diverse physical contexts, this thesis will try to be as detailed and self-contained as necessary, providing a clear exposition of the underlying concepts and technical aspects.
Studying the low-temperature phases of doped Hubbard models, including the emergence of collective order and exotic normal phases, is at the heart of strongly correlated physics. This thesis offers new theoretical insights into the low-energy physics of doped Hubbard models, with a particular emphasis on leveraging quantum simulation as a powerful investigative tool. We explore the emergence of collective order driven by many-body interactions, by predicting and observing stripe-like structures in quantum gas microscopes of engineered Hamiltonians. These fluctuating stripe patterns are developed into a theoretical framework for the pseudogap— a highly enigmatic phase in hole-doped cuprates—where we show how fluctuating domain walls yield effective toric code descriptions. Ultracold atoms in optical lattices provide a unique platform for directly probing and testing this theory. We further investigate unconventional bilayer nickelate superconductors, predicting an exceptionally stable superfluid state in a single-band Hubbard model at experimentally accessible temperatures. By proposing schemes to observe coherent pair-pair correlations, this advances the long-standing goal of realizing and observing long-range superconducting order in ultracold atomic systems in optical lattices. On non-bipartite lattices, we examine kinetic magnetism in Hubbard models and moiré heterostructures. Additionally, the low-temperature regime of doped Hubbard models with enhanced symmetries is analyzed, revealing exotic phenomena such as sub-dimensional polaronic particles. We develop machine learning techniques to extract key physical insights from many-body snapshots, offering a new avenue for understanding intricate quantum phases. Finally, we go beyond the Fermi-Hubbard paradigm and show how non-local strongly correlated models can be leveraged to address classical optimization problems through quantum annealing.
Understanding the physics underlying high-temperature superconductivity in cuprates and, more recently, infinite-layer nickelates has remained a central challenge in condensed-matter physics. We establish neural quantum states (NQS), specifically Hidden Fermion Determinant States (HFDS), as a scalable variational approach to the three-band Emery model of the copper- and nickel-oxide layers in these materials. After benchmarking HFDS against matrix product states on width-two geometries, we study ground states of fully two-dimensional (2D) systems of up to 10×10 unit cells (300 sites). We characterize the momentum-space distribution of dopants and find a pronounced electron-hole dichotomy similar to cuprate experiments. We further downfold the three-band model to effective single-band descriptions by constructing interacting Wannier functions. We consider a wide range of parameters -- from the charge-transfer regime relevant to cuprates to the Hubbard-Mott regime of nickelates, as well as systematic scans of the charge-transfer gap that has been demonstrated to impact the critical superconducting temperatures. Across all regimes, the effective model significantly deviates from the usual Fermi-Hubbard model: The typical ratio U/t is enhanced, some parameters experience a significant doping dependence, and sizable terms beyond the conventional Hubbard model are present, most notably a density-assisted hopping tn. Notably, in all effective models, tn has the largest contribution to particle-hole asymmetry, rather than next-nearest-neighbor hopping contributions. The effective parameters sensitively depend on the charge-transfer energy, doping, and interaction ratios. Our results establish HFDS as an efficient tool for studying the 2D Emery model and demonstrate that single-band descriptions can require interaction terms generated by the underlying multi-band models.
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.
The microscopic origin of high-temperature superconductivity in cuprates remains one of the central open questions in condensed matter physics. Growing experimental and theoretical evidence suggests that the bare single-band Fermi-Hubbard model may not fully capture properties of cuprates such as superconductivity, motivating us to revisit the canonical three-band model of the copper-oxide planes - the Emery model - from which the single-band counterpart was originally derived. Here, we propose and analyze a quantum simulation scheme for realizing the Emery model in regimes relevant to cuprates and infinite-layer nickelates with today's ultracold atom quantum simulation platforms, enabling the exploration of the three-band physics on system sizes that are challenging for current numerical methods. Specifically, we show that a two-dimensional optical lattice with a superimposed pattern of repulsive potentials can be designed to study low-temperature properties for variable parameter regimes of the Emery model relevant to cuprates as well as infinite-layer nickelates. Our results pave the way for real material simulations with ultracold atom quantum simulators and a better understanding of the physics of unconventional superconductors.
Achieving materials-specific predictions for large, realistic molecules and solids with strong electron correlations remains a long-standing challenge in quantum chemistry. This dissertation develops scalable ab initio quantum many-body methods for crystalline materials, demonstrating that rigorous optimization of theoretical approximations and numerical algorithms enables predictive computation even in strongly correlated systems. The work tackles three interconnected challenges, namely describing material-specific properties of strongly correlated superconductors, achieving linear scaling with k-points for large-scale periodic calculations, and establishing reliable methods for electron-phonon interactions. The following chapters address each challenge in turn. Chapter 2 demonstrates that ab initio density matrix embedding theory, combined with symmetry-breaking strategies for superconducting order parameters, reproduces experimental trends in cuprate superconductivity, including pressure and layer effects on transition temperatures. By directly solving the electronic Schrödinger equation from material structures, these calculations capture multi-orbital covalency effects that simplified model Hamiltonians neglect, revealing their essential role in the spin fluctuations driving pairing. This predictive capability establishes a foundation for efficient computational screening of superconducting materials. Extending these calculations to larger k-point meshes and broader phase diagram explorations, however, demands more efficient computational algorithms. To overcome this computational bottleneck, Chapter 3 introduces interpolative separable density fitting framework. This development enables thermodynamic limit calculations with up to 1000 k-points, as validated on diamond, carbon dioxide, nickel monoxide, and cuprate systems. Integration with density matrix embedding theory and local natural orbital methods further yields converged ground-state energies from accurate correlated wavefunction methods such as CCSD(T) for crystalline materials in the thermodynamic limit. With computational efficiency established, the remaining challenge lies in extending the theoretical framework beyond purely electronic degrees of freedom. Chapter 4 addresses this need by establishing exponential ansatz wavefunctions as competitive approaches for electron-phonon systems. Unlike previous treatments based on perturbation theory, systematic benchmarking of coupled cluster theory and variational Lang-Firsov methods on the Holstein model demonstrates, for the first time, that these approaches accurately describe polaron formation across coupling regimes when combined with appropriate reference state optimization. These results provide a foundation for incorporating phonon effects into ab initio studies of superconducting materials. In addition to these methodological advances, GPU acceleration and MPI parallelization enhance computational throughput, enabling efficient large-scale calculations. Together, these developments constitute a computational framework for predictive ab initio quantum many-body calculations in crystalline materials, opening new avenues for understanding and designing strongly correlated quantum materials.