Theory of Quantum Antiferromagnets

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A comprehensive theoretical study will be made of the novel properties of frustrated, doped, and random quantum antiferromagnets. Recent inelastic neutron scattering measurements have provided us with a wealth of information on the spin dynamics of the doped cuprates: a successful unraveling of the nature of the spin fluctuations is clearly important to a deeper understanding of the novel properties of these high temperature superconductors. With the aim of understanding these measurements, we will study the universal properties of two-dimensional antiferromagnets in the vicinity of a zero temperature phase transition at which the long- range magnetic order vanishes. The effects of doping, quenched randomness, incommensurate spin fluctuations, and incipient phase separation on this phase transition and the quantum disordered phase will be examined. Other frustrated, layered antiferromagnets have also been studied in recent years: in particular, the kagome lattice is a strong, experimentally realizable candidate for displaying a disordered ground state. We will undertake a theoretical study of these systems: the nature of quantum phase transitions and the quantum disordered phases of antiferromagnets on frustrated two-dimensional lattices will be studied by a duality analysis and mappings to dimer models. Finally, the low temperature magnetic propoerties of the metallic and insulating phases of doped semiconductors will be studied: these materials are well described by a strongly random Hubbard model which will be examined by numerical and analytic approaches. %%% Theoretical research will be conducted on magnetic models which are at the core of problems related to strongly interacting physical systems such as the high temperature superconductors. These problems are at the forefront of present research in condensed matter physics.