Research - Barry Friedman
My research interests are in computational and theoretical condensed matter and chemical physics. Recently, I have been interested in quantum Hall systems, in particular in the computational aspects. A quantum Hall system consists of electrons moving in 2 dimensions in a high magnetic field at low temperatures. A physical realization is GaAs heterostuctures. One fascinating aspect of these systems is the possibility of having quasi particles with non abelian statistics. Materials with non abelian quasi particles provide a possible robust implementation of quantum computation. Hence, the behavior of condensed matter systems at low temperatures and large distances can be just as exotic as the behavior of particles studied at high energy by elementary particle physicists.
Several Sam Houston State University undergraduate physics majors and myself have investigated quantum Hall systems with a number of numerical tools. To compute the wave functions, direct diagonalization and the density matrix renormalization group have been used. The numerical problem is that the quantum mechanical state space, practically speaking the matrices one must deal with, grow as an exponential of the number of particles being simulated. Even if a many body electron wave function can be accurately calculated it is still not easy to understand the physics. Therefore, special quantities are needed to characterize the wave functions. In particular, quantities from quantum information theory have proved to be valuable; these quantities include the entanglement entropy and the topological entanglement entropy. An outstanding question in this area, that our studies have addressed, are the nature of the states in the second Landau level and whether these states have non abelian quasiparticles.