Navigating Frustration

Cornell University, Ithaca NY

Investigators

Abstract

TECHNICAL SUMMARY This award supports theoretical research and education on frustrated materials. The PI aims to develop new theoretical tools and concepts to handle frustrated spins and interacting fermions with a focus on various scenarios of dilution in frustrated models. Research will be performed in the following directions: (1) Theoretical methods will be developed to find non-coplanar classical ground states for antiferromagnets in lattices with competing spin interactions beyond nearest neighbors. The effective Hamiltonian due to anharmonic quantum fluctuations will be computed for the kagome and hyperkagome/garnet lattices. The "Coulomb phase" paradigm will be applied to systems with disorder that itself obeys a divergence-like constraint. (2) The PI will simulate non-Abelian height models with different discrete groups, and characterize the interactions between defects as a function of the defect charge. (3) The PI will study Heisenberg antiferromagnets at percolation. He will work out the scaling of nonlinear products of the discrete Laplacian eigenmodes on fractal critical percolation clusters. The ordering and low-energy excitations of quantum antiferromagnets at percolation will be studied by renormalization group methods. (4) The PI will investigate the ground state and excitations of the Fendley-Schoutens supersymmetric model with spinless fermions. This research provides an environment for training graduate students in advanced theoretical methods and concepts, and for providing research experiences at the frontiers for undergraduate students. NONTECHNICAL SUMMARY This award supports theoretical research and education on materials in which the electrons exhibit frustration. Frustration arises when the interactions between electrons give conflicting signals, often due to the geometry of the crystal lattice. Since the interactions fail to lead to an obvious single state, the system somehow chooses among seemingly equally good states. The thrust of this research is to advance understanding of how this happens. In many real materials, missing atomic sites or impurities provide small perturbations that can have a dramatic effect on the state of the electrons in the material. The PI will also study this effect. The research involves developing theoretical methods and concepts to advance understanding of frustrated materials. The study of these materials may lead to the discovery of new states of electronic matter which lie outside of textbook states like magnetism and standard notions of a quantum electronic liquid that permeates a lattice of atomic nuclei. This is fundamental research which contributes to the intellectual foundations of new technologies and the discovery of new materials. This research provides an environment for training graduate students in advanced theoretical methods and concepts, and for providing research experiences at the frontiers for undergraduate students.