This award was made on a proposal submitted to the Division of Materials Research under the Information Technology Research solicitation NSF-04-012. Research activities covered by this award fall under the National Priority Area, "Advances in Science and Engineering," and the Technical Focus Area, "Innovation in Computational Modeling or Simulation in Research." This award supports computational and theoretical research to develop a new algorithm, a "two-step" density-matrix renormalization group method, and to apply this algorithm and the dynamical cluster approximation to the simulation of strongly correlated electron and spin models of highly anisotropic materials. The new algorithm begins with a perturbation expansion in transverse coupling having properties that are known from rigorous theorems. Well known techniques such as exact diagonalization or the density-matrix renormalization group (DMRG) method will be used to obtain the low energy spectrum of isolated chains. The anisotropic 2D Hamiltonian is then projected onto a tensor product of states yielding an effective 1D Hamiltonian which can be studied by the DMRG. Preliminary work suggests that the method can predict an ordered phase starting from a disordered phase. Important theoretical issues that have so far resisted other methods will be addressed. These are: (i) the role of frustration in weakly coupled Heisenberg spin chains as models for low dimensional quantum antiferromagnets, (ii) the role of the magnetic field and the possible occurrence of superconductivity in the ground state of weakly coupled Hubbard chains as models for organic superconductors, and (iii) the spectral properties of weakly-coupled Hubbard chains as models for inorganic conductors. This project also involves an educational component. A non-physics major course will be developed. It will be based on the use of simple simulations and visualizations of computer experiments to "bring to life" essential concepts in various physics fields ranging from simple mechanics to astrophysics. The PI's algorithm may lead to new insights into the physics of strongly correlated electron materials generally. It may have applications to specific materials beyond those studied in this project and may have impacts in other fields. The understanding of interaction effects in low dimensional quantum antiferromagnets and frustration may have impact on efforts to develop quantum computers and magnetic refrigerants, potential replacements for chlorofluorocarbons which pose environmental concerns. Computer codes created in the course of this research will be made available to other researchers through the web and public software repositories. %%% This award was made on a proposal submitted to the Division of Materials Research under the Information Technology Research solicitation NSF-04-012. Research activities covered by this award fall under the National Priority Area, "Advances in Science and Engineering," and the Technical Focus Area, "Innovation in Computational Modeling or Simulation in Research." This award supports computational and theoretical research to develop a new algorithm that will be used to study strongly correlated electron and spin models of highly anisotropic materials. Understanding strongly correlated electron materials has proven to be very intellectually challenging and has resulted in the discovery of new physics. The PI focuses on materials that contain one-dimensional "chains" in which the electrons are strongly interacting. Interactions between the chains are much weaker. Examples include lithium purple bronze, and various organic conductors like TMTSF. The PI will exploit the structure of these materials and powerful numerical methods to devise a new computationally accessible technique and use it to study unusual electronic states that arise from correlated motion of electrons in these inherently low-dimensional systems. This project also involves an educational component. A non-physics major course will be developed. It will be based on the use of simple simulations and visualizations of computer experiments to "bring to life" essential concepts in various physics fields ranging from simple mechanics to astrophysics. The PI's new algorithm may lead to new insights into the physics of strongly correlated electron materials generally. It may have applications to specific materials beyond those studied in this work and may have impacts in other fields. The understanding of interaction effects in low dimensional quantum antiferromagnets and frustration may have impact on the quest to develop quantum computers and magnetic refrigerants, potential replacements for chlorofluorocarbons which pose environmental concerns. Computer codes created in the course of this research will be made available to other researchers through the web and public software repositories. ***
