This grant supports theoretical research into fundamental condensed matter physics. Understanding the behavior of interacting many-particle quantum systems is one of the central intellectual challenges of our time. Electrons in metals, which give rise among other things to conductivity, superconductivity and magnetism, are a particularly important and challenging class of interacting many-particle quantum system. Our present understanding is based on Landau's "Fermi liquid theory" which shows how, in many cases, the apparently complicated behavior of the electron liquid may be understood in terms of a picture of weakly interacting "quasiparticles." However, it has become clear over the years that Landau's picture fails to describe the behavior of a wide class of metals, including those displaying interesting and potentially important behavior such as high temperature superconductivity, and extremely large magnetoresistance. The research conducted here is aimed at developing the physical understanding, along with the analytical and computational techniques, needed to understand the "non-fermi-liquid" behavior of systems not adequately described by conventional concepts.
One central focus of this research is "quantum criticality," the behavior occurring when the ground state of a material changes from one phase to another. Materials near a phase transition point typically exhibit large amplitude, long-ranged, slowly changing fluctuations, which are empirically known to lead to particularly pronounced non-fermi-liquid behaviors. Further, the long spatial and temporal range of these fluctuations means that they are amenable to analytical study using established techniques in quantum field theory. An ongoing theme of this research is the use of these techniques to study strong forms of non-fermi-liquid behavior with the goal of extracting general insights and developing techniques which may carry over to other problems.
A characteristic feature of metals is the presence of a large density of low-lying excitations, which means that fluctuations are typically damped - their energy is dissipated into creating metallic excitations. The interplay of quantum mechanics and dissipation is a fundamental and still ill-understood issue: it is hoped that this research will lead to new insights into the issue, both via solution of quantum critical problems arising in the metallic context and via new calculations combining the analytical techniques mentioned above with techniques for dealing with effects of dissipation on a single quantum particle.
A second focus of the research is the development and application of numerical techniques for determining thermodynamics and dynamics of systems and circumstances not adequately described by Landau's quasiparticle theory or its extensions. Theoretical developments over the past decade associated with the concept of "dynamical mean field theory" suggest dramatic improvements in our ability to calculate excitation spectra and response functions. Research will be undertaken into extending and improving these techniques, and in applying them to understand experiments in a wide range of novel materials.
Students and postdoctoral associates will be closely involved in this research. %%% This grant supports theoretical research into fundamental condensed matter physics. Understanding the behavior of interacting many-particle quantum systems is one of the central intellectual challenges of our time. Electrons in metals, which give rise among other things to conductivity, superconductivity and magnetism, are a particularly important and challenging class of interacting many-particle quantum system. Our present understanding is based on Landau's "Fermi liquid theory" which shows how, in many cases, the apparently complicated behavior of the electron liquid may be understood in terms of a picture of weakly interacting "quasiparticles." However, it has become clear over the years that Landau's picture fails to describe the behavior of a wide class of metals, including those displaying interesting and potentially important behavior such as high temperature superconductivity, and extremely large magnetoresistance. The research conducted here is aimed at developing the physical understanding, along with the analytical and computational techniques, needed to understand the "non-fermi-liquid" behavior of systems not adequately described by conventional concepts.
Students and postdoctoral associates will be involved in this research. ***
