Restricted Scope for Participant Support: CAREER: Novel States of Correlated Quantum Matter in Numerical Simulations, Field Theories and Natural Systems

A thorough theoretical understanding of the possible phases that microscopic quantum models of condensed matter physics can realize at zero temperature is an important frontier in fundamental physics. This understanding has vast applications to natural systems, especially relevant to the rich behavior of the large number of complex materials that have been synthesized in laboratories in recent years. Due to improved sample quality and modern experimental techniques, a large amount of high quality data is available, a quantitative and even often qualitative explanation for which relies on solving complex many body problems. Unfortunately, even the simplest interacting quantum many body problems are intractable either analytically or numerically without making uncontrolled approximations. An exciting prospect for progress in non-perturbative solutions of quantum many body physics, is the powerful combination of numerical simulations of microscopic models in an "unbiased" way on large lattices (using methods such as quantum Monte Carlo (QMC, density matrix renormalization group and exact diagonalization), with field theoretic methods (such as renormalization group, large-N and E-expansions, mean field theory). I propose to carry out research at the interface of these directions: numerical simulations, field theoretic methods and analysis of experimental data, to address novel problems in correlated quantum condensed matter physics. Some of the key topics addressed in this proposal are, • quantum criticality in two-dimensional anti-ferromagnets • understanding experiments on frustrated magnetism in complex materials • the role of impurities in strongly correlated systems • development of new global update schemes for QMC algorithms • improvement of our understanding of the "sign problem" of QMC and broadening the class of sign problem free models Broader Impact: The proposed research will further our understanding of fundamental problems in quantum physics and at the same time provide the basis for understanding many experiments carried out worldwide. Advances in our knowledge of novel quantum phenomena in complex materials will clearly facilitate the use of such materials in future technologies. Part of the proposed research has direct applications to experiments carried out at University of Kentucky's EPSCoR supported Center for Advanced Materials, and a large fraction of the proposed research makes extensive use of the facilities at the University of Kentucky's EPSCoR supported Center for Computational Sciences (CCS), thus strengthening the efforts of the University and NSF to have centers of excellence in the commonwealth of Kentucky. A new course for graduate and advanced undergraduate students at UK on computational physics will be developed and taught. The course will be a platform to create top quality computational researchers and facilitate better usage of the CCS facilities. The proposed budget will support two graduate students, educate them in modern computational and analytic techniques in my group and give them an opportunity to interact with other first-class research groups at UK, neighboring institutions and worldwide. Research projects with undergraduate students at UK will be offered and participation in a program (STEM-plus) to improve physics high school teachers in the state of Kentucky will be undertaken. Concrete measures are underway to involve students and professors from neighboring non-PhD granting institutions in my research program, in specific, and physics in general. These efforts include reaching out to students at the unique Berea College, where roughly one third of the student body represents an ethnic minority. A Kentucky wide physics day is also planned so that physics majors from different colleges in KY can meet each other and form a network, while learning about the first rate research carried out at UK.