Simulating and machine learning quantum criticality in a nearly antiferromagnetic metal

In the last few decades, quantum criticality in itinerant electron systems has become a central focus of condensed matter physics. On the one hand, it represents a candidate mechanism for high-temperature superconductivity. On the other hand, it can lead to a breakdown of Fermi liquid theory. The formation of a comprehensive understanding of metallic quantum criticality has, however, been significantly hampered by the fact that in many-fermion systems, fluctuations of a critical order parameter can couple to extensive gapless modes on a finite Fermi surface. This interplay, while giving rise to intriguing physical phenomena, leads to strong electronic correlations, which are notoriously difficult to handle by analytic methods. In this thesis, we investigate metallic quantum criticality by means of large-scale quantum Monte Carlo simulations and contribute unbiased, rigorous results to the discussion. Focusing on antiferromagnetic spin-density wave ordering, we present the numerically exact phase diagram of a spin-fermion model whose solution has so far been out of reach. In particular, we highlight the emergence of high-temperature d-wave superconductivity and rigorously establish the quantum critical properties of the antiferromagnetic quantum critical point. Combining the Monte Carlo method with a quantum loop topography approach, we demonstrate that important features of quantum critical metals can be autonomously identified by machine learning of current-current correlations. This allows us to analyze the electronic transport characteristics of two quantum critical metals, including the spin-fermion model, over a large parameter range and leads to the identification of extended non-Fermi liquid regimes in their respective phase diagrams.