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

TL;DR

This paper introduces a recursion relation for second-quantized Halperin states in fractional quantum Hall systems, enabling analysis without exact diagonalization and confirming the states as zero modes with correct filling factors.

Contribution

It provides a novel recursion formula for second-quantized Halperin states, simplifying their study and validation in fractional quantum Hall effect research.

Findings

Recursion relation accurately generates Halperin states

States are confirmed as zero modes of the Hamiltonian

Correct filling factors are verified

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.