Quantum Hall Ground States and Regular Graphs

DOI10.1016/J.NUCLPHYSB.2022.116018arXiv1807.01811MaRDI QIDQ6303863

Hamed Pakatchi

Publication date: 4 July 2018

Abstract: We show that every uniform state on the sphere is essentially a superposition of regular graphs. In addition, we develop a graph-based ansatz to construct trial FHQ ground states sharing the local properties of Jack polynomials. In particular, our graphic states have the $(k,r)$ clustering property. Moreover, a subclass of the construction is realizable as the densest zero-energy state of a model that modifies the projection Hamiltonian.

Mathematics Subject Classification ID

Nuclear physics (81V35) Estimates of eigenvalues in context of PDEs (35P15) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Feynman integrals and graphs; applications of algebraic topology and algebraic geometry (81Q30) Many-body theory; quantum Hall effect (81V70) Cluster sets, prime ends, boundary behavior (30D40)

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