Relations between density-density correlators of states in the maximal spin multiplet

TL;DR

The paper derives identities linking density-density correlators within the maximal spin multiplet, enabling energy calculations of various fractional quantum Hall states from the highest-weight state correlations.

Contribution

It introduces new identities that relate correlation functions across the multiplet, simplifying energy computations for FQH states.

Findings

Analytical energy expressions for Halperin (1,1,1) state as a function of density imbalance.

Numerical evaluation of energies for multiple FQH states.

Simplified computation of density-density correlations across the multiplet.

Abstract

We present identities relating the pair-correlation functions and static structure factors of states in the maximal spin multiplet. This allows us to compute these density-density correlation functions of all members of the multiplet using just these correlation functions of the highest-weight state. We apply these relations to obtain energies for many fractional quantum Hall (FQH) states. In particular, we analytically compute the energies of the Halperin-$(1,1,1)$ state as a function of density imbalance and layer separation, and numerically evaluate these energies for many other FQH states.