This award supports theoretical and computational research and education to study quantum Hall systems. The PI will focus on computing the phase diagram of the N=1 and N=2 Landau levels, using the density matrix renormalization group, with and without disorder. Questions that will be addressed include the nature of the stripe state near half-filling in the N=2 Landau level and whether the incompressible states in the N=1 Landau level at 5/2 and 12/5 have non abelian statistics. Direct contact with experiment will be made through calculations of dynamical correlation functions that will be compared with microwave spectroscopy of quantum Hall stripe and bubble phases. Two undergraduate students per year will be involved in this work. With careful supervision, this educational experience in condensed matter physics can lead to meaningful contributions to the project and to encouragement for students to pursue further education in areas of advanced technology that are crucial to the future economic well being of the United States.
NON-TECHNICAL SUMMARY: This award supports theoretical and computational research and education. The PI will carry out a computational study of quantum Hall systems. Quantum Hall systems consist of many electrons confined to two dimensions at low temperatures in the presence of a strong magnetic field. Due to these extreme physical conditions, the electrons influence each other very strongly; there is strong electron-electron correlation. The result of the strong electron-electron correlation is the formation of fascinating collective states. Recent theoretical advances suggest that computation can be performed by manipulating particular quantum Hall states; a computer based on this phenomenon would be more powerful than existing computers for certain important applications. Quantum Hall states are very interesting from the viewpoint of fundamental science. The PI aims to discover new physical laws that arise due to the collective behavior of ordinary electrons. Since electron-electron interaction plays such an important role, numerical methods are crucial in understanding quantum Hall systems. One of the most powerful numerical methods for treating many electron states is the density matrix renormalization group developed originally for one dimensional models. The PI will use this method and state of the art computers to perform accurate large simulations. The ability to treat as many electrons as possible is often essential when studying collective behavior. Two undergraduate students per year will be involved in this work. With careful supervision, this educational experience in condensed matter physics can lead to meaningful contributions to the project and to encouragement for students to pursue further education in areas of advanced technology that are crucial to the future economic well being of the United States.
