Quantum Monte Carlo Simulations of Quantum Criticality and Topological Phases

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TECHNICAL SUMMARYThis award supports theoretical and computational research, and education to advance understanding of quantum materials pertaining to quantum criticality in fermionic systems, the origin of incoherence across quantum phase transitions, and emergent topological phases in the presence of spin-orbit coupling and strong correlations. The PI's general approach is to develop models that contain the essence of the phenomena mentioned above, and to investigate them by a variety of methods, including quantum Monte Carlo simulations. This research also has impact on the field of ultracold atomic gases that have emerged as excellent laboratories for gaining insights into quantum materials. Major breakthroughs that the PI hopes to make in the course of this project are:(i) a quantitative understanding of how a Fermi surface and associated quasiparticle excitations are destroyed near a quantum critical point;(ii) an understanding of the origin of dissipation and emergence of novel conducting but incoherent metallic phases near a quantum phase transition;(iii) emergence of a superfluid with non-trivial spatial, spin and topological ordering in a system with spin-orbit coupling and strong correlations;(iv) a library of fully developed state-of-the-art QMC codes, including (a) worm algorithm and maximum entropy methods for large-scale boson simulations providing information about dynamical susceptibilities; (b) wavefunction based variational Monte Carlo methods with optimization of large numbers of parameters; and (c) reputation QMC methods that minimize the dependence on the wavefunction.This project also supports training students in the setting of a diverse research group working to advance understanding of quantum matter and materials. The PI plans to organize a Festival of Physics at the Columbus Science Museum on the theme of random numbers "Raisins to Pi." The PI is spearheading the Scientific Thinkers program Meet a Scientist, Be a Scientist, and Learn about other Scientists at the Innis Elementary School in the Columbus City School district. The PI will launch a website for undergraduate-level education with short 10 minute lecture-nuggets that are searchable and coordinate her efforts with other options for distance learning. Non-Technical abstract:This award supports theoretical and computational research, and education on novel emergent states of matter and on quantum phase transitions between them. Materials are made up of many electrons and ions and the interactions among them lead to new states of matter, such as superconductors and magnets, which arise from the self-organization of the electrons, their motion, and their intrinsic magnetic orientation known as spin. The PI will investigate the possibility that novel phases could emerge when the spin of the electron is locked to its motion. When interactions between the particles are strong enough to dominate over the energy due to their motion, their kinetic energy, textured magnetic phases with hedgehog, vortex and spiral structures may result. Electrons moving in the background of magnetic textures lead to unusual properties of materials related to the transport of electrons. The PI will also explore quantum phase transitions. These are phase transformations that take place at the absolute zero of temperature. It is believed that these transitions may have consequences that may reach up to a significant fraction of room temperature. Unlike the familiar phase transformation from water to steam which is driven by thermal fluctuations, quantum phase transitions are driven by quantum fluctuations which arise from Heisenberg's famous uncertainty principle. Quantum phase transitions may lead to dramatic changes such as the restructuring of one quantum state to a completely different one upon changing the interactions between particles, or the application of a magnetic field, or pressure. These questions of fundamental importance will be explored in the context of physical models that have direct relevance to oxide materials containing transition metal as well as ultracold atoms in trapped in lattices of light. This project also supports training students in the setting of a diverse research group working to advance understanding of quantum matter and materials. The PI plans to organize a Festival of Physics at the Columbus Science Museum on the theme of random numbers "Raisins to Pi." The PI is spearheading the Scientific Thinkers program Meet a Scientist, Be a Scientist, and Learn about other Scientists at the Innis Elementary School in the Columbus City School district. The PI will launch a website for undergraduate-level education with short 10 minute lecture-nuggets that are searchable and coordinate her efforts with other options for distance learning.