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Second-quantized approach to the study of Halperin state in fractional quantum Hall effect

Li Chen, Zhiping Yao

Abstract

We give a recursion relation for the second-quantized fermionic (bosonic) Halperin state, which avoids exact diagonalization of its two-component first-quantized parent Hamiltonian. We validate this formula by proving that the second-quantized Halperin state, as recursively defined in this formula, is indeed a zero mode of the corresponding second-quantized parent Hamiltonian and that it has the correct filling factor.

Second-quantized approach to the study of Halperin state in fractional quantum Hall effect

Abstract

We give a recursion relation for the second-quantized fermionic (bosonic) Halperin state, which avoids exact diagonalization of its two-component first-quantized parent Hamiltonian. We validate this formula by proving that the second-quantized Halperin state, as recursively defined in this formula, is indeed a zero mode of the corresponding second-quantized parent Hamiltonian and that it has the correct filling factor.
Paper Structure (8 sections, 43 equations)

This paper contains 8 sections, 43 equations.

Table of Contents

  1. Introduction
  2. Second-quantized fermionic (bosonic) Halperin state
  3. Halperin state and its parent Hamiltonian
  4. Recursive formula for fermionic (bosonic) Halperin state
  5. Proof that recursively defined Halperin state satisfies zero mode conditions \ref{['zo1']}, \ref{['zo2']} and \ref{['zo3']}
  6. Root state and filling factor of fermionic (bosonic) Halperin state
  7. Conclusion and Discussion
  8. The derivation of Eq. (\ref{['rere']}) from the first-quantized wave function