Contents

# Contents

## Idea

In quantum physics a Laughlin wavefunction is a certain Ansatz for an n-particle wavefunction which is meant to capture at least aspects of ground states with anyonic properties, such as for the levels in the quantum Hall effect.

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## References

### General

The original article:

• Robert B. Laughlin, Anomalous Quantum Hall Effect: An Incompressible Quantum Fluid with Fractionally Charged Excitations, Phys. Rev. Lett. 50 (1983) 1395 $[$doi:10.1103/PhysRevLett.50.1395$]$

Review:

• Steven M. Girvin, Section 2.1 of: Introduction to the Fractional Quantum Hall Effect, Séminaire Poincaré 2 (2004) 53–74, reprinted in The Quantum Hall Effect, Progress in Mathematical Physics 45, Birkhäuser (2005) $[$pdf, doi:10.1007/3-7643-7393-8_4$]$

• Chetan Nayak, Steven H. Simon, Ady Stern, Michael Freedman, Sankar Das Sarma, Section III.D.2.c (pp. 1125) of: Non-Abelian Anyons and Topological Quantum Computation, Rev. Mod. Phys. 80 1083 (2008) $[$arXiv:0707.1888$]$

• David Tong, Section 3.1 of: The Quantum Hall Effect (2016) $[$course webpage, pdf, pdf$]$

• Roman Remme, The Laughlin Wavefunction, talk notes (2017) $[$pdf, pdf$]$

See also:

Characterization as a braid representation:

A “hierarchy” of Laughlin-like states:

### Laughlin wavefunctions as conformal blocks

• Gregory Moore, Nicholas Read, Section 2.2 of: Nonabelions in the fractional quantum hall effect, Nuclear Physics B 360 2–3 (1991) 362-396 $[$doi:10.1016/0550-3213(91)90407-O, pdf$]$

• Xiao-Gang Wen, Non-Abelian statistics in the fractional quantum Hall states, Phys. Rev. Lett. 66 (1991) 802 $[$doi:10.1103/PhysRevLett.66.802, pdf$]$

• B. Blok, Xiao-Gang Wen, Many-body systems with non-abelian statistics, Nuclear Physics B 374 3 (1992) 615-646 $[$doi:10.1016/0550-3213(92)90402-W$]$

• Xiao-Gang Wen, Yong-Shi Wu, Chiral operator product algebra hidden in certain fractional quantum Hall wave functions, Nucl. Phys. B 419 (1994) 455-479 $[$doi:10.1016/0550-3213(94)90340-9$]$

Review in the broader context of the CS-WZW correspondence:

Specifically for logarithmic CFT:

Specifically for su(2)-anyons:

Last revised on February 20, 2023 at 17:59:20. See the history of this page for a list of all contributions to it.