Theoretical research will be conducted on condensed matter systems with strong correlations. The research is awarded under the umbrella of the NSF-wide Mathematical Sciences Priority Area. Merits of the research include understanding systems with qualitatively new behavior, such as have arisen in studies of magnets with frustrating interactions, high-temperature superconductors, and topological quantum computation. This work will utilize field-theoretic techniques, especially non-perturbative methods useful for understanding novel phases which cannot be approached by conventional methods. The research will include: continuing to derive exact results for topological phases, where quasiparticle excitations do not have the quantum numbers of the electron, i.e., are fractionalized; discovering and describing quantum critical points which separate novel phases from phases with conventional order; probing more deeply the symmetry structure of one-and two-dimensional models of strongly correlated electrons; using integrable field theory in quantum impurity problems.
The principle investigator has extensive experience in developing and utilizing modern techniques. Successful applications of these techniques in current research include: deriving many exact results for the widely-studied classical and quantum dimmer models; exploring in depth the phase diagrams of models with topological phases; utilizing supersymmetry to describe the ground state of strongly correlated electron systems; describing different kinds of density-wave order in models with competing interactions, such as in a model of bosons in a one-dimensional optical lattice; deriving exact results for models with disorder; deriving correlation functions and other exact results for Haldane-gap spin chains; understanding Fano resonances in quantum dots and atomic systems.
In a broader context, this type of research is pushing condensed matter theory into brand new arenas. In these systems, the traditional Landau paradigm of treating quasiparticles as electron-like does not give even a good qualitative description of the physics, much less an accurate quantitative prediction. It is important that the field broaden and develop new ideas and methods to attack these problems.
An even broader impact will come from a book being written entitled Up Against the Infinite. This book will explain to general audiences the new sorts of theories used to probe physics in extreme conditions, e.g., ultra-low temperature, code-cracking quantum computers, the early universe, and how the renormalization group links physics at vastly different length scales. %%% Theoretical research will be conducted on condensed matter systems with strong correlations. The research is awarded under the umbrella of the NSF-wide Mathematical Sciences Priority Area. Merits of the research include understanding systems with qualitatively new behavior, such as have arisen in studies of magnets with frustrating interactions, high-temperature superconductors, and topological quantum computation.
A broader impact of the grant will come from a book being written entitled Up Against the Infinite. This book will explain to general audiences the new sorts of theories used to probe physics in extreme conditions, e.g., ultra-low temperature, code-cracking quantum computers, the early universe, and how the renormalization group links physics at vastly different length scales. ***
