Exact relations between the density-density correlators of states in a spin multiplet
TLDR
Exact identities relate density-density correlators in spin multiplets, enabling computation for all states from the highest-weight state.
Key contributions
- Discovers exact identities for density-density correlators in spin multiplets.
- Allows computing all multiplet state correlators from the highest-weight state.
- Applies these relations to determine energies of various Fractional Quantum Hall (FQH) states.
- Provides analytical energies for Halperin-(1,1,1) state and numerical for other FQH states.
Why it matters
This paper introduces a powerful theoretical framework to simplify calculations for complex quantum states. It significantly reduces the computational burden for understanding Fractional Quantum Hall states and their properties, offering new insights into many-body physics.
Original Abstract
We present exact identities relating the pair-correlation functions and static structure factors of states in a 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.
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