Simulation Studies of Ground State Phases and Criticality in Correlated Quantum Matter

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NONTECHNICAL SUMMARYThis award supports theoretical research and education on developing methods and algorithms for the simulation of electronic states in materials. Materials derive their properties from their microscopic building blocks: atoms and molecules. In typical metals, a fraction of the electrons disassociate from individual atoms and migrate through the system, while in other materials all electrons remain localized. In either case, the electrons give materials the electric and magnetic properties that are exploited in electronics and other technological applications. This project aims at increasing our understanding of the ways in which electrons can form a wealth of different complex states due to their interactions with each other. The interactions are electromagnetic in nature, and depend on the environment in which the electrons are embedded, i.e. the specific material and its external conditions. In the same way as water can appear in three different common phases (liquid, gas, and solid), electrons can also transition between states with completely different properties by changing their environment, e.g. by applying pressure or an external magnetic field. Being microscopic particles, the motion and interactions of electrons are governed by quantum mechanics, and it is technically extremely challenging to construct tractable theoretical models to describe them, and to understand and exploit their different phases and properties. In this project, a set of models relevant to materials with localized electrons are studied via large-scale computer simulations. The arrangement of the spins (magnetic moments) of the electrons in different patterns is determined by how they interact with each other. At the heart of the project is understanding the way a state having a pattern of ordered spins can "melt", i.e. go into a disordered state, or go into another type of ordered state. Progress in fundamental understanding is important for achieving further fundamental advances as well as applications.In addition to its scientific goals, the project involves training graduate students in state-of-the-art modeling and computer simulations, and creating user-friendly software for other researchers by applying the methods and models developed. The PI is also involved in broader training activities, through continued involvement in summer schools and similar educational events.TECHNICAL SUMMARYThis award supports theoretical research and education on developing methods and algorithms for the simulation of electronic states in materials.Lattice quantum magnets play an important role in quantum many-body physics, and offer many opportunities for studying collective behavior beyond classical statistical mechanics. In this project, minimalistic lattice models are used to capture universal phenomena of experimental and theoretical relevance, and unbiased numerical tools are employed to obtain conclusive results for generic properties of ground states, excitations, and critical scaling. In the absence of rigorous analytical solutions, such numerically exact results are invaluable as cornerstones of our understanding of quantum materials. An interrelated set of investigations are proposed to address some of the most intriguing aspects of quantum phase transitions beyond the conventional Landau-Ginzburg-Wilson paradigm. Unbiased numerical simulations will be carried out on several lattice models in which a second length scale appears alongside the conventional correlation length upon approaching a quantum critical point.Building on previous work, a scaling hypothesis involving two simultaneously divergent length scales at the AFM-VBS transition will be further tested within the class of J-Q models proposed previously by the PI, with the goal of firmly establishing the proposed relationships between exponents appearing in finite-size and finite-temperature scaling forms. Moreover, a new class of quantum clock models are proposed as a potentially simpler class of systems in which to investigate and understand the origin of the anomalous two-length scaling. More detailed studies of J-Q models will also be carried out, including studying the effects of disorder at the critical point and in the two ordered phases. In order to facilitate QMC studies of dynamic properties, work will be carried out on a stochastic analytic continuation method, which shows promise towards delivering better frequency resolution than other analytic continuation methods used so far.In addition to its scientific goals, the project involves training graduate students in state-of-the-art modeling and computer simulations, and creating user-friendly software for other researchers by applying the methods and models developed. The PI is also involved in broader training activities, through continued involvement in summer schools and similar educational events.