CDS&E: Quantum Monte Carlo Methods for Electron Correlations and Spin-Orbit Effects in Low-Dimensional Materials

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NON-TECHNICAL SUMMARYThis award supports theoretical and computational research on properties and behavior of interacting quantum systems. This is one of the most impactful frontiers of current condensed matter and materials physics. In particular, low-dimensional structures with sizes of the order of a nanometer (one billionth the size of a meter) with various competing interactions between the electrons and their spatial and spin degrees of freedom offer new and unprecedented opportunities for the development of new materials and devices with ultralow power consumption and ultrafast processing speeds. The key barrier that hampers the realization of this potential is our limited knowledge of how to efficiently and accurately describe, modify and control the relevant quantum mechanisms. The PI and his group will focus on high-performance computational approaches for solving the underlying fundamental equations and establish a new set of tools for analysis of quantum phenomena and for discovery of new materials made up of nanometer-sized components. The proposed methodology is based on an optimized combination of sophisticated analytical constructions, robust and effective simulation approaches, and high performance of large parallel computing platforms. The computational developments will become a part of an open source simulation package for use by research communities at large. Inherent part of the effort will be the training of a graduate student in advanced simulation methods and the physics of nanometer-sized systems. Such training is expected to provide multiple opportunities for a future career in scientific research. The educational impact of this research will be further enhanced through expansion of the curriculum at North Carolina State University by developing a graduate computational physics course with emphasis on simulations of quantum systems and related topics with broad interest across physics, chemistry, materials and engineering disciplines.TECHNICAL SUMMARY This award supports computational and theoretical research focused on the development of computational quantum Monte Carlo methods for studies of low-dimensional materials. First, novel approaches for constructions of many-body pairing wave functions will be established using effective Hamiltonians with explicit inclusion of pairing effects based on pair density matrices. This will provide the key inputs for correlated trial wave function constructions in a robust and systematic manner so that electron correlations will be described consistently across varying spin-polarizations and symmetries. As a result, the quantum Monte Carlo accuracy for important quantities such as binding and dissociation energies, spin gaps, and excitations will increase very significantly when compared with mainstream electronic structure approaches. Second, quantum Monte Carlo methods for treating spins as genuine quantum variables will be developed and implemented for routine use in calculations of systems with important spin interactions. This development will break new ground in electronic structure calculations and will make studies of materials with significant spin-orbit effects and systems with non-collinear spins or topologically ordered states possible in a many-body wave function setting. The planned applications and prototypes target promising research challenges in low-dimensional and spintronic nanomaterials such as doped graphene and related systems. The computational developments will become a part of an open source simulation package for use by research communities at large. Inherent part of the effort will be the training of a graduate student in advanced simulation methods and the physics of nanometer-sized systems. Such training is expected to provide multiple opportunities for a future career in scientific research. The educational impact of this research will be further enhanced through expansion of the curriculum at North Carolina State University by developing a graduate computational physics course with emphasis on simulations of quantum systems and related topics with broad interest across physics, chemistry, materials and engineering disciplines.