Algebraic approach to fractional quantum Hall effect
We construct an algebraic description for the ground state and for the static response of the quantum Hall plateaus with a filling factor ν = N / ( 2 N + 1 ) in the large N limit. By analyzing the algebra of the fluctuations of the shape of the Fermi surface of the composite fermions, we find th...
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| Format: | Journal article |
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American Physical Society
2018
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| Summary: | We construct an algebraic description for the ground state and for the static response of the quantum Hall plateaus with a filling factor ν = N / ( 2 N + 1 ) in the large N limit. By analyzing the algebra of the fluctuations of the shape of the Fermi surface of the composite fermions, we find the explicit form of the projected static structure (SSF) factor at large N and fixed z = ( 2 N + 1 ) q ℓ B ∼ 1 , where q is the wave number at which the system is probed, and ℓ B is the magnetic length. When z < 3.8 , we obtain the exact universal formula for the projected SSF. The formula does not depend on the particular form of the Hamiltonian. |
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