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

TL;DR

This paper investigates non-equilibrium charge transport in the non-Abelian $ u=5/2$ quantum Hall state using DMRG, revealing how the system transitions between different fixed points under varying voltage.

Contribution

It introduces a DMRG-based approach to analyze non-equilibrium tunneling in non-Abelian quantum Hall states, extending methods to finite voltage conditions.

Findings

Confirmed the transition from coupled to decoupled edges at low voltages.

Validated the approach by reproducing known results for the $ u=1/3$ state.

Demonstrated consistency with perturbation theory at extreme voltages.

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.