Quantum cluster methods and their applications to quantum materials

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Our understanding of materials has long been based on simple paradigms: metals can be understood in terms of quasi-independent electrons, undergoing occasional collisions; at the other extreme, magnets are understood in terms of the spins of localized electrons. But between these paradigms lies a spectrum of materials that defy comprehension in terms of these simple pictures, even though they may show characteristics of both. High-temperature superconductors are the prototype of such "strongly correlated quantum materials". Such materials can display a variety of fascinating properties, from superconductivity to exotic magnetism, charge ordering, transitions between insulating and conducting behavior, spontaneous violation of the time-reversal symmetry, etc. Technological advances based on these properties will be guided by a deeper understanding of strongly correlated quantum materials at a fundamental level. The objective of this proposal is two-fold: (1) to develop computational tools to understand and calculate properties of strongly correlated quantum materials and (2) to apply these methods to a variety of systems, some generic, other representing real materials. Even the simplest theoretical models that we can devise to describe these materials cannot be solved with the traditional theorist's pen and paper. They require the use of supercomputers and of sophisticated approximation strategies. Part of our effort is to make our understanding of quantum materials more quantitative, by using models that are closer to real materials, or by applying our methods with a higher degree of accuracy. Another part of our effort is to make the relevant computational tools easier to use and widely available. Physical systems that we propose to study include high-temperature superconductors, superconducting strontium ruthenate, twisted bilayer graphene, heterostructures made of high-temperature superconductors and topological insulators. Computational tools that we propose to improve on include cluster dynamical mean field theory and tensor network methods. This is a program of fundamental, not applied research. Much of today's economy rests on fundamental discoveries made many decades ago (e.g. semiconductors). Private foundations (e.g. the Moore foundation and the Simons foundation in the US) understand the importance of investing in fundamental research on new materials, even though decades may be necessary before applications of these materials are commonplace. Students trained within this research program will develop skills that will be useful in a wide range of research activities, both fundamental and applied: critical thinking, computational skills, data analysis, etc.