scholarly journals Fractional Quantum Hall Effect in a Relativistic Field Theory

2020 ◽  
Vol 124 (13) ◽  
Author(s):  
David B. Kaplan ◽  
Srimoyee Sen
Keyword(s):  
Field Theory ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Fractional Quantum Hall Effect ◽  
Relativistic Field ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Relativistic Field Theory

COLLECTIVE FIELD THEORY APPLIED TO THE FRACTIONAL QUANTUM HALL EFFECT

1991 ◽  
Vol 05 (01n02) ◽  
pp. 417-426
Author(s):  
B. Sakita ◽  
Dong-Ning Sheng ◽  
Zhao-Bin Su
Keyword(s):  
Field Theory ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Constraint Equation ◽  
Dynamical Theory ◽  
Fractional Quantum Hall Effect ◽  
Fractional Quantum ◽  
Free Vortex ◽  
Fractional Quantum Hall

We present an application of collective field theory to the fractional quantum Hall effect (FQHE). We first express the condition, that the electrons are all in the lowest Landau level, as a constraint equation for the state functional. We then derive the fractional filling factor from this equation together with the no-free-vortex assumption. A hierarchy of filling factors is derived by using the particle-vortex dual transformations. In the final section we discuss an attempt at a dynamical theory of FQHE, which would justify the no-free-vortex assumption. A derivation of Laughlin’s wave function with and without quasi-hole excitations is also given.

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