# Effective edge state dynamics in the fractional quantum Hall effect

@article{Fern2018EffectiveES, title={Effective edge state dynamics in the fractional quantum Hall effect}, author={Richard L. Fern and R. Bondesan and S. Simon}, journal={Physical Review B}, year={2018}, volume={98}, pages={155321} }

We consider the behavior of quantum Hall edges away from the Luttinger liquid fixed point that occurs in the low-energy, large-system limit. Using the close links between quantum Hall wave functions and conformal field theories, we construct effective Hamiltonians from general principles and then constrain their forms by considering the effect of bulk symmetries on the properties of the edge. In examining the effect of bulk interactions on this edge, we find remarkable simplifications to these… Expand

#### Figures and Tables from this paper

#### 5 Citations

Entanglement Action for the Real-Space Entanglement Spectra of Composite Fermion Wave Functions

- Physics
- 2021

We argue and numerically substantiate that the real-space entanglement spectrum (RSES) of composite fermion quantum Hall states is given by the spectrum of a local boundary perturbation of a (1 + 1)d… Expand

Wavefunctionology: The Special Structure of Certain Fractional Quantum Hall Wavefunctions

- Physics
- 2021

Certain fractional quantum Hall wavefunctions — particularly including the Laughlin, Moore-Read, and Read-Rezayi wavefunctions — have special structure that makes them amenable to analysis using an… Expand

Is the composite fermion state of Graphene a Haldane's Chern insulator?

- Physics
- 2018

The properties of interacting electrons in a half-filled Landau level are well addressed by the Halperin-Lee-Read (HLR) picture of non-interacting composite fermions. We discuss how such a… Expand

Almost linear Haldane pseudopotentials and emergent conformal block wave-functions in a Landau level

- Physics
- 2019

We consider a two dimensional (2D) model of particles interacting in a Landau level. We work in a finite disk geometry and take the particles to interact with a linearly decreasing two-body Haldane… Expand

Topology- and symmetry-protected domain wall conduction in quantum Hall nematics

- Physics
- Physical Review B
- 2019

We consider domain walls in nematic quantum Hall ferromagnets predicted to form in multivalley semiconductors, recently probed by scanning tunnelling microscopy experiments on Bi(111) surfaces. We… Expand

#### References

SHOWING 1-10 OF 43 REFERENCES

Nonabelions in the fractional quantum Hall effect

- Physics
- 1991

Applications of conformal field theory to the theory of fractional quantum Hall systems are discussed. In particular, Laughlin's wave function and its cousins are interpreted as conformal blocks in… Expand

THEORY OF THE EDGE STATES IN FRACTIONAL QUANTUM HALL EFFECTS

- Physics
- 1992

The dynamical theory of the edge excitations of generic fractional quantum Hall (FQH) states is summarized and expanded. The low energy effective theory of the edge excitations for the most general… Expand

Structure of edge-state inner products in the fractional quantum Hall effect

- Physics
- 2018

We analyze the inner products of edge state wave functions in the fractional quantum Hall effect, specifically for the Laughlin and Moore-Read states. We use an effective description for these inner… Expand

Conformal invariance of chiral edge theories

- Physics
- 2009

The low-energy effective quantum field theory of the edge excitations of a fully-gapped bulk topological phase corresponding to a local interaction Hamiltonian must be local and unitary. Here it is… Expand

Electrodynamical properties of gapless edge excitations in the fractional quantum Hall states.

- Physics, Medicine
- Physical review letters
- 1990

The electrodynamical properties of the edge excitations in the fractional quantum Hall (FQH) states are studied and a practical way to probe the topological orders in the FQH states is shown. Expand

Chiral Luttinger liquid and the edge excitations in the fractional quantum Hall states.

- Physics, Medicine
- Physical review. B, Condensed matter
- 1990

The edge excitations are shown to form a new kind of state which is called the Chiral Luttinger Liquid (´LL), which clearly demonstrate the non-Fermi liquid behaviors of the FQH states. Expand

Nonlinear quantum shock waves in fractional quantum Hall edge states.

- Physics, Medicine
- Physical review letters
- 2006

This work shows that the transport in interacting nondissipative electronic systems is essentially nonlinear and unstable and discusses perspectives of observation of quantum shock waves and a direct measurement of the fractional charge in fractional quantum Hall edge states. Expand

Edge excitations of paired fractional quantum Hall states.

- Physics, Medicine
- Physical review. B, Condensed matter
- 1996

The Hilbert spaces of the edge excitations of several “paired” fractional quantum Hall states, namely the Pfaffian, Haldane-Rezayi and 331 s are constructed and the states at each angular momentum level are enumerated and the wavefunctions for each case have a similar form. Expand

Fractional quantum Hall states of atoms in optical lattices.

- Physics, Medicine
- Physical review letters
- 2005

The dynamics of the atoms in the lattice is analogous to the motion of a charged particle in a magnetic field if an oscillating quadrupole potential is applied together with a periodic modulation of the tunneling between lattice sites. Expand

Quantum Hall wave functions based on S 3 conformal field theories

- Physics
- 2010

We construct a family of quantum Hall Hamiltonians whose ground states, at least for small system sizes, give correlators of the ${S}_{3}$ conformal field theories. The ground states are considered… Expand