Theoretical limits, legacies, and prospects: Types of physics involved and kinds of problems that might be solved - What can the Fermi-Hubbard model teach about metal-insulator transitions, magnetism, exotic superconductivity, and materials like transition metal monoxides, cuprates, heavy fermions?

摘要

Metals and insulators are very different states of matter. Both, however, are characterized by stable and robust electronic states, among which the electrons rearrange themselves, as one varies the temperature or applies external fields. This simplicity affords excellent--textbook grade--understanding of these materials, but it also limits our ability to "tweak" them, i.e. to significantly alter their behaviors through modest perturbations. Much more interesting are materials that find themselves somewhere in between. In this Metal-Insulator Transition (MIT) region, spectacular response is observed with modest tuning of control parameters, often displaying "Strange" or "Bad Metal" behavior. In these systems, which include the familiar (yet still poorly understood) doped semiconductors, but also various transition metal oxides and many other families of correlated matter, the appealing physical picture of nearly-free electrons fail in dramatic ways. Here one observes dramatic evolution and modification of the electronic spectra with modest variation of temperature, pressure, doping or--what is of most technological relevance--gating, indicating pronounced many-body effects. The task to understand and to describe how the electronic states respond and adjust, as one tunes the system from insulator to metal, this is a basic science challenge of our era.