Understanding the Laughlin wave function for the fractional quantum Hall effect

2002 ◽  
Vol 70 (4) ◽  
pp. 401-405 ◽  
Author(s):  
B. L. Johnson
Keyword(s):  
Wave Function ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Fractional Quantum Hall Effect ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Laughlin Wave Function

scholarly journals A non-Abelian parton state for the $ν=2+3/8$ fractional quantum Hall effect

2021 ◽  
Vol 10 (4) ◽  
Author(s):  
Ajit Coimbatore Balram
Keyword(s):  
Wave Function ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Ground State ◽  
Topological Structure ◽  
Quantum Hall ◽  
Fractional Quantum Hall Effect ◽  
Fractional Quantum ◽  
Fractional Quantum Hall

Fascinating structures have arisen from the study of the fractional quantum Hall effect (FQHE) at the even denominator fraction of 5/25/2. We consider the FQHE at another even denominator fraction, namely \nu=2+3/8ν=2+3/8, where a well-developed and quantized Hall plateau has been observed in experiments. We examine the non-Abelian state described by the ``\bar{3}\bar{2}^{2}1^{4}3‾2‾214" parton wave function and numerically demonstrate it to be a feasible candidate for the ground state at \nu=2+3/8ν=2+3/8. We make predictions for experimentally measurable properties of the \bar{3}\bar{2}^{2}1^{4}3‾2‾214 state that can reveal its underlying topological structure.

THE CHERN-SIMONS-LANDAU-GINZBURG THEORY OF THE FRACTIONAL QUANTUM HALL EFFECT

1992 ◽  
Vol 06 (05n06) ◽  
pp. 803-804 ◽  
Author(s):  
Shou Cheng Zhang
Keyword(s):  
Wave Function ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Mean Field ◽  
Fractional Quantum Hall Effect ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Physical Consequences ◽  
Chern Simons

This paper[1] gives a systematic review of a field theoretical approach to the fractional quantum Hall effect (FQHE) that has been developed in the past few years[2, 3]. We first illustrate some simple physical ideas to motivate such an approach and then present a systematic derivation of the Chern-Simons-Landau-Ginzburg (CSLG) action for the FQHE, starting from the microscopic Hamiltonian. It is demonstrated that all the phenomenological aspects of the FQHE can be derived from the mean field solution and the small fluctuations of the CSLG action. Although this formalism is logically independent of Laughlin’s wave function approach, their physical consequences are equivalent. In particular, it is shown that the Laughlin’s wave function can be ”derived” from the CSLG theory under reasonable approximations. The CSLG theory demonstrates a deep connection between the phenomena of superfluidity and the FQHE, and can provide a simple and direct formalism to address many new macroscopic phenomena of the FQHE.

THE COULOMB GAS FOR EXCITED STATES IN THE FRACTIONAL QUANTUM HALL EFFECT

1991 ◽  
Vol 05 (19) ◽  
pp. 1307-1311
Author(s):  
M. HILKE ◽  
M. RUIZ-ALTABA
Keyword(s):  
Wave Function ◽  
Hall Effect ◽  
Excited States ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Coulomb Gas ◽  
Fractional Quantum Hall Effect ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Set Up

We follow Fubini's suggestion to use vertex operators for describing electrons and holes in the two-dimensional set-up appropriate for the description of the fractional quantum Hall effect, i.e., on the gauge-fixed magnetic plane. Laughlin's wave function is thus reproduced as the correlator of primary conformal fields, represented as exponentials of a free scalar field. We generalize an Ansatz by Halperin and present a new wave function describing the ground-state and the excited states of a system of unpolarized electrons. We realize these wave functions as correlators of normal-ordered exponentials of two free fields. We also give an explicit representation for the creation operator of an excitation.

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