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

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TECHNICAL SUMMARY:This award supports theoretical research and education in computer simulation studies of ground state phases and criticality in correlated quantum matter. Large-scale computer simulations of lattice quantum many-body systems are carried out in this work. These studies are inspired by the phenomenology of strongly-correlated electron systems?their complex phase diagrams and quantum phase transitions in particular?but are not complete descriptions of specific materials (because of the computational complexity). Instead, simplified quantum spin models are used to capture physical phenomena of interest and gain generically valid insights through unbiased simulations. Complex ground states and phase transitions induced by competing interactions are studied, focusing in particular on the transition between an antiferromagnetic (AF) and a valence-bond-solid in two-dimensional quantum spin systems. The transition and the VBS phase are investigated using sophisticated numerical methods. Research into novel computational algorithms based on states defined by tensor-networks and related objects are also carried out. Such methods have the potential to enable studies of ground states of previously intractable frustrated quantum spin systems.The effort undertaken has broader impacts with both scientific and educational consequences. The work on numerical simulation techniques produces new algorithms that have broad applications in condensed matter physics and atomic and molecular physics (ultra-cold condensates). The work on tensor-network and related states for describing correlated quantum states is also of interest in quantum information theory. An educational aspect of this proposal, beyond the important training of students in physics and advanced scientific computing, is a web-site in which a variety of computational methods developed by the PI are presented in a pedagogical manner, along with example programs for a variety of models.NONTECHNICAL SUMMARY:This award supports theoretical research and education in the use of state-of-the-art computer simulation studies of novel electronic structures that have been discovered in exotic materials like the two-dimensional carbon sheets called graphene. Large-scale computer simulations of quantum physics that describes these systems are carried out in this work. These studies are inspired by experiments and discovery of these novel materials, but are not aimed at complete descriptions of specific materials because such detailed numerical studies are not yet possible because of the computational complexity. Instead, simplified quantum spin models are used in order to capture physical phenomena of interest, with the objective of gaining new generically valid insights through unbiased computer simulations. The effort undertaken has broader impacts with both scientific and educational consequences. The work on computer simulations produces new algorithms that have broad applications in condensed matter physics and atomic and molecular physics (ultra-cold condensates). The work on novel computational algorithms is also important in quantum information theory. An educational aspect of this proposal, beyond the important training of students in physics and advanced scientific computing, is a web-site in which a variety of computational methods developed by the PI are presented in a pedagogical manner, along with easy-to-use example programs for a variety of models.