In collaboration with Thors Hans Hansson (SU) and Juha Suorsa (Nordita). Electrons in a Magnetic Field. Semi-classically, electrons in a strong magnetic.
Hall viscosity of hierarchical quantum Hall states[1] or What is the viscosity of the ν =
2 5
state?
Mikael Fremling Fysikum, Stockholm University (SU) In collaboration with Thors Hans Hansson (SU) and Juha Suorsa (Nordita)
Electrons in a Magnetic Field
Overlap as a Function of τ2
Semi-classically, electrons in a strong magnetic field move on cyclotron orbits. This motion gives each electron an orbital spin s.
A Case Study at ν =
2 5
We study the state at ν = 2/5 on the torus. On the plane the wave function is known and written as an antisymmetrization over two groups {z}, {w } and the wave function P P − 41 ( i |z|2 + i |w |2i )
ψPlane = eY
× Y ∂w i (zi − wj )2 ×
i
i,j
Y Y 3 (zi − zj ) (wi − wj )3. i 1 then D1,0 is dominant, while at τ2 < 1 then D0,1 is dominant. The linear combination D1,0 + D0,1 is better than either of the terms on their own.
Good Overlap in the Entire τ -plane
1 (1) η = ~¯n¯s , 2 as a non-zero (antisymmetric) viscosity coefficient η. Here n¯ is the electron density, and ¯s the mean orbital spin. This viscosity coefficient is non-zero only in two dimensions and for time-reversal broken systems, such as the QH system.
The derivates i ∂wi are important since they make the antrisymmetrization differentiate between w and z. Without them the whole wave function vanishes identically. We seek a formulation of ΨQon the torus, and especially, the analouge of i ∂wi .
Torus Electronic Wave Functions We construct electronic wave functions by computing a correlation function of vertex operators in conformal field theory and extract the physical wave functions as linear combinations of conformal blocks. The wave function for ν = 25 is − 14 (
