Non-equilibrium transport through a point contact in the $ν=5/2$ non-Abelian quantum Hall state

Details Non-equilibrium transport through a point contact in the $ν=5/2$ non-Abelian quantum Hall state Non-equilibrium transport through a point contact in the $ν=5/2$ non-Abelian quantum Hall state

2008-09-08

arxiv.org/abs/0809.1415v2

Phys. Rev. Lett 101 (2008): 236801

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

Scientific paper

10.1103/PhysRevLett.101.236801

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. We map this problem to resonant tunneling between attractive Luttinger liquids and use the time-dependent density-matrix renormalization group (DMRG) method to compute the current through the point contact in the presence of a {\it finite voltage difference} between the two edges. We confirm that, as the voltage is decreases, the system is broken into two pieces coupled by electron hopping. 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 non-equilibrium current through a point contact in a $\nu=1/3$ quantum Hall state, confirming the Bethe ansatz solution of the problem.

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