This award supports theoretical research and education on new states of electronic matter in materials. Materials derive their properties from their microscopic building blocks; atoms and molecules, and, in particular, the electrons that we often envision as swirling around atomic nuclei. In 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 electrical and magnetic properties that are exploited in electronics components 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 depend on the specific material which hosts the electrons. Being microscopic particles, the motion and interactions of electrons are governed by quantum mechanics, and it is technically challenging to construct tractable theoretical models to describe them, and to understand and tailor their properties. In this project, models of interacting electrons are studied under conditions relevant to, for example, high temperature superconductor materials formed by copper-oxide layers separated from each other by other atoms. In these materials electrons form a new state of matter, superconductivity, which can conduct electricity without loss or resistance at temperatures where oxygen would be a liquid. The models are studied using large-scale computer simulations. At the heart of the project is to understand how an insulating magnet is transformed into new magnetic states when a model parameter, for example describing electron interaction, is changed, and how additional electrons injected into this state behave. Understanding this model system may be key to understanding the physical origins of superconductivity in these materials and may provide a key to the discovery of new materials which exhibit superconductivity at higher temperatures opening avenues to technological applications such as low loss power transmission and new kinds of electronic devices. In addition to its scientific significance, the project aims to train graduate students in state-of-the-art physical modeling and computer simulations, and to help develop user-friendly software for other researchers applying the methods and models developed.
This award supports theoretical research and education on new states of electronic matter in materials. An important aspect of condensed matter physics is to study ground states and excitations of strongly correlated quantum-matter systems for example, localized spins of highly frustrated quantum magnets or valence electrons of cuprate high temperature superconductors. Quantum field-theory descriptions often contain emergent ingredients, such as spinons, holons, and gauge fields, which are proposed on the basis of phenomenology and symmetry arguments. The field theories are typically only solvable in certain limits. This research focuses on utilizing numerically exact quantum Monte Carlo techniques to study microscopic Hamiltonians, which can be tuned to various regimes where emergent particles and fields can be detected by studying low-energy physics. These studies can be related to field-theory results, and also can yield experimentally detectable signatures of unconventional collective electronic states. This research can therefore bridge lattice-scale physics and emergent low-energy behavior, with potential impact on theoretical as well as experimental research on correlated quantum matter. The PI will study J-Q models in which the magnetically ordered ground state of a 2D quantum antiferromagnet can be destroyed, leading to a quantum phase transition to a non-magnetic state with emergent local singlets that form a valence-bond solid. These models appear to host unconventional low-energy quantum objects which can be interpreted as spinons and a U(1) gauge field. The PI will address how these particles and fields emerge from the lattice scale up to large length-scales accessible with powerful simulation techniques tailored to the models. The main objectives are: (i) To relate the excitations of J-Q models to gauge field theory, in particular to explore analogies of the Higgs mechanism and Higgs boson in systems close to the quantum phase transition between the antiferromagnet and the valence-bond solid. (ii) To introduce mobile charge carriers which presumably would lead to holons, and explore connections with the "strange metal" state of the cuprate high temperature superconductors. New and improved simulation algorithms will be developed as an integral part of the project and these have broad applications in condensed matter physics as well as in research on ultra-cold atomic condensates and systems of interest in the quantum information research. The models and methods are also of interest in high-energy particle physics, providing a simpler setting than standard lattice gauge-field theory to study non-perturbative quantum many-body physics.
