This theoretical research will study magnetic properties of materials and provide model-based computational support for experimental characterization tools such as Raman scattering, neutron scattering and nuclear magnetic resonance (NMR). The bulk of the study relies on two types of computational methods applied to many-body model Hamiltonians.
The first is the series expansion method, which is based on developing high order perturbation theory or power-series expansions for thermodynamic properties in a suitable variable such as inverse temperature or ratio of coupling constants. When these expansion parameters are small and the series are convergent, a direct summation provides the desired answer. Pade approximants and related extrapolation methods are used to obtain thermodynamic quantities when the expansion parameters become large. These methods are known to work well provided one develops a long enough series and does not cross any phase boundaries. The singular properties associated with the phase transitions can be obtained as a limiting behavior from specially developed extrapolation schemes.
The second method is quantum Monte Carlo simulations based on the stochastic series expansion technique. This is a stochastic method to sum up all the terms in a high temperature expansion of the partition function. Using recently developed "operator loop" updates, this method allows one to study fairly large finite-size systems down to low temperatures.
These theoretical calculations will be used to study properties of novel and existing magnetic materials. These include the cuprate family of high temperature superconducting materials and several other organic and inorganic materials. We identify a number of recently synthesized square-planar antiferromagnetic materials and spatially anisotropic materials exhibiting unusual behavior, whose properties will be addressed. In order to have a greater impact on the understanding of real materials, we plan to continue our collaborations with electronic structure theorists and experimental groups.
A second objective of this research is to develop, establish or confirm new ideas and concepts in strongly interacting many-particle systems. For example, the question of whether fluctuation dominated one-dimensional physics can carry over to higher dimensional systems will be addressed. Another question of interest is whether there exist two-dimensional spin models, with exotic phases and possibly fractional spin excitations. Specific models, whose properties will be calculated, are discussed.
A third objective is to further develop and extend the computational methods themselves so that they can be used for a wider class of models and for a larger class of experimental properties. We will focus on dynamical properties of magnetic systems at finite temperatures, which would be most important in quantitatively understanding neutron scattering and NMR results.
These computational studies provide excellent training for students and postdoctoral associates. %%% This theoretical research will study magnetic properties of materials and provide model-based computational support for experimental characterization tools such as Raman scattering, neutron scattering and nuclear magnetic resonance (NMR). The bulk of the study relies on two types of computational methods applied to many-body model Hamiltonians. These are series-expansion techniques and quantum Monte Carlo methods. These studies provide excellent training for students. ***