Publisher’s Note: Charge Fractionalization in the Integer Quantum Hall Effect [Phys. Rev. Lett. 112, 166801 (2014)]

Quench-induced entanglement and relaxation dynamics in Luttinger liquids

“…However, in sharp contrast with the NESF, here the non-universal transient contributions decay as t −ν−1 and t −ν−2 for the charge and energy currents respectively, with ν ≥ 1 given in Eq. (20). This behavior of the non-universal contribution is not surprising since, in essence, A < (V, t) ∝ ∂ V η I η (V, t) and A < (V, t) ∝ ∂ 2 V η P η (V, t).…”

“…In the context of interacting 1D systems, it is well established that their low-energy equilibrium properties are described by the Luttinger liquid (LL) model [30][31][32]. They exhibit peculiar effects stemming from their non-Fermi liquid nature due to inter-particle interactions, such as charge and spin fractionalization [19,20,[32][33][34][35][36][37][38][39][40][41][42]. In recent years the LL model has also been proven to be a very powerful tool for studying the dynamics of 1D systems after a quench of the interaction strength.…”

“…Among all, the recent technological developments in atomic and condensed matter physics offer a very promising platform to investigate these important issues. Nowadays it is indeed possible to prepare a quantum system in a given non-equilibrium state and to study its evolution in real time, for instance by using cold atoms [11][12][13][14][15], trapped ions [16][17][18], or even quantum conductors in solid-state devices [19,20]. An intriguing possibility to drive a quantum system out of equilibrium is to perform a quantum quench, i.e.…”

Luttinger liquids, Fermi liquids, and fractional statistics

“…The fractionalization is linked to chiral separation of charges that are introduced in the system 11,12 , so that fractions of a unit charge move to the right and the left, respectively. There has in particular been interest in the study of this effect for edge excitations in quantum Hall systems, where interactions between edge modes give rise to the charge fractionalization [7][8][9][10] . However, one should note the important difference between the charge fractionalization effect in the bulk of the quantum Hall system and at the edges.…”

Unexpected tunneling current from downstream neutral modes

“…Since then, significant effort has been devoted to using shot noise measurements to gain insight into more complicated edges. [13][14][15][16][17][18][19][20][21][22][23][24][25] The experiment of Ref. 8 consists of a Hall bar with a QPC across which noise and current are measured, as shown in Fig 1. Current is then injected into one edge, downstream of the QPC (here downstream always refers to the net direction of charged current), and the change in current and shot noise are measured.…”