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

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. 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.

References in corpus (6)

• Real time evolution using the density matrix renormalization group
• Particle-hole symmetry and the Pfaffian state
• Particle-Hole Symmetry and the $\nu =5/2$ Quantum Hall State
• Time-step targetting methods for real-time dynamics using DMRG
• Transport properties and Kondo correlations in nanostructures: the time-dependent DMRG method applied to quantum dots coupled to Wilson chains
• Dynamical Disentanglement across a Point Contact in a Non-Abelian Quantum Hall State

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