$\mathbb{Z}_k^{(r)}$-Algebras, FQH Ground States, and Invariants of Binary Forms

DOI10.1016/J.NUCLPHYSB.2022.116010arXiv2104.05777MaRDI QIDQ6365123

Publication date: 12 April 2021

Abstract: A prominent class of model FQH ground states is those realized as correlation functions of

m a t h b b Z_{k}^{(r)}

-algebras. In this paper, we study the interplay between these algebras and their corresponding wavefunctions. In the hopes of realizing these wavefunctions as a unique densest zero energy state, we propose a generalization for the projection Hamiltonians. Finally, using techniques from invariants of binary forms, an ansatz for computation of correlations

l a n g l e p s i (z_{1}) c d o t s p s i (z_{2 k}) a n g l e p r o d_{i < j} (z_{i} - z_{j})^{2 r / k}

is devised. We provide some evidence that, at least when

r = 2

, our proposed Hamiltonian realizes

m a t h b b Z_{k}^{(2)}

-wavefunctions as a unique ground state.

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Operator algebra methods applied to problems in quantum theory (81R15)

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