This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).
This award in the Condensed Matter and Materials Theory program supports research in theoretical condensed matter physics that will study the quantum mechanical states in fractional quantum Hall liquids, which are one of the landmark discoveries of the past twenty five-years. Recent numerical and experimental evidence indicates the possibility of an even more exotic variant of these systems, so-called nonabelian quantum Hall states. The latter may provide the proper hardware for a fault tolerant topological quantum computer. Although many powerful approaches exist to describe quantum Hall systems, our understanding of non-abelian states is still limited compared to that of abelian states, due to the far greater complexity of the former.
The main goal of the research is to establish a simple and efficient language in which problems in abelian and non-abelian quantum Hall systems can be formulated and attacked. This language makes explicit use of the effectively one-dimensional structure of the Hilbert space of low lying excitations in a strong magnetic field. Concrete topics include the derivation of non-abelian statistics from wavefunctions, the discussion of phase transitions in multi-component quantum Hall systems, the derivation of edge physics via a new "constructive" method for abelian and non-abelian fractional quantum Hall systems, and the derivation of constraints for the quantum numbers of abelian and non-abelian quantum Hall phases within the formalism discussed in this proposal.
The broader impact of this research will be the availability of a more pedagogical language in which abstract concepts in quantum Hall research and topological quantum computing, such as "fractional charge", "topological sector", and "fusion rules", can be communicated more easily to people with an undergraduate physics background. This will help interested students to start research in this fascinating field earlier, and will make the field more universally accessible to non-physicists. The latter will be of paramount importance should a topological quantum computer be built. The projects described in this proposal will give rise to multiple research opportunities for students at the graduate and advanced undergraduate level.
NONTECHNICAL SUMMARY This award in the Condensed Matter and Materials Theory program supports research in theoretical condensed matter physics that will study the quantum mechanical states in fractional quantum Hall liquids, which are one of the landmark discoveries of the past twenty five-years. An exotic variant of these systems, so-called nonabelian quantum Hall states, may provide systems appropriate for constructing a fault tolerant topological quantum computer. Exploring the feasibility of fault tolerant quantum computing is one of the major efforts in the physics community today.
The broader impact of this research will be the availability of a more pedagogical language in which abstract concepts in quantum Hall research and topological quantum computing, such as fractional charge, can be communicated more easily to people with an undergraduate physics background. This will help interested students to start research in this fascinating field earlier, and will make the field more universally accessible to non-physicists. The latter will be of paramount importance should a topological quantum computer be built. The projects described in this proposal will give rise to multiple research opportunities for students at the graduate and advanced undergraduate level.
