Second-quantized approach to the study of Halperin state in fractional quantum Hall effect
Phys. Rev. B 113, 235133 – Published 18 June, 2026
DOI: https://doi.org/10.1103/mbbh-9ftj
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.
