Paul Fendley

Abstract:

We analyze charge-e/4 quasiparticle tunneling between the edges of a point contact in a non-Abelian model of the nu = 5/2 quantum Hall state in the presence of a finite voltage difference using the time-dependent density-matrix renormalization group method. We confirm that, as the voltage decreases, the system is broken into two pieces. In the limits of small and large voltage, we recover the results expected from perturbation theory about the infrared and ultraviolet fixed points. We test our methods by finding the analogous nonequilibrium current through a point contact at nu = 1/3.

Abstract:

We study a model of strongly correlated electrons on the square lattice which exhibits charge frustration and quantum critical behavior. The potential is tuned to make the interactions supersymmetric. We establish a rigorous mathematical result which relates quantum ground states to certain tiling configurations on the square lattice. For periodic boundary conditions this relation implies that the number of ground states grows exponentially with the linear dimensions of the system. We present substantial analytic and numerical evidence that for open boundary conditions the system has gapless edge modes.