We develop a general algebraic scheme to decompose fractional quantum Hall (FQH) wave functions based on the operator contraction multiplication. By introducing fermionic and bosonic operators and establishing three fundamental contraction rules, we achieve an exact decomposition of the Laughlin states. This approach naturally extends to multicomponent systems by factorizing coupled Jastrow factors via resultants and elementary symmetric polynomials, enabling a complete decomposition of the Halperin states. For the Halperin (2,2,1) state, we explicitly derive its basic expansion, identify root configurations, and reveal intra- and intercolor squeezing operators, thereby uncovering the underlying generalized Pauli principle. Using this method, we compute orbital entanglement spectra for up to 16 particles with decomposition dimensions exceeding ${10}^{11}$, obtaining edge excitation sequences that precisely match chiral Luttinger liquid theory. Our framework breaks through the long-standing limitations of Jack polynomials, provides a unified decomposition for both single- and multicomponent FQH states, and opens an alternative avenue for exploring wave functions for more complex FQH states.

Close

PrevNext

View figure in article

• Fractional quantum Hall effect
• Strongly correlated systems
• Two-dimensional electron system
• Trial wave functions