An Algebraic Approach to FQHE Variational Wave Functions

S. B. Mulay1, John J. Quinn2, Mark Shattuck3
1Department of Mathematics, University of Tennessee, Knoxville, TN 37996, USA
2Department of Physics, University of Tennessee, Knoxville, TN 37996, USA
3Institute for Computational Science & Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam

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Alexandersson, P., Shapiro, B.: Discriminants, symmetrized graph monomials, and sums of squares. Experiment. Math. 21, 353–361 (2012)

Brouwer, A.E., Draisma, J., Popoviciu, M.: The degrees of a system of parameters of the ring of invariants of a binary form. arXiv: 1404.5722

Dixmier, J.: Quelques résultats et conjectures concernant les séries de Poincaré des invariants des formes binaires. In: d’algèbre, S., Dubreil, P., Malliavin, M.-P. (eds.) 36ème année (Paris, 1983-1984). Lecture Notes in Math., 1146, pp 127–160. Springer, Berlin (1985)

Elliot, E.B.: An Introduction to the Algebra of Quantics, 2nd edn. Chelsea Publishing Company, New York. (1913), reprint (1964)

Grace, J.H., Young, A.: The Algebra of Invariants. Chelsea Publishing Company, New York (1964). (1903), reprint

Greenhill, C., McKay, B.D.: Asymptotic enumeration of sparse multigraphs with given degrees. SIAM J. Discret. Math. 27, 2064–2089 (2013)

Hansson, T.H., Hermanns, M., Simon, S.H., Viefers, S.F.: Quantum Hall physics: Hierarchies and conformal field theory techniques. Rev. Mod. Phys. 89, 025005 (2017)

Jain, J.K.: Composite-Fermion approach for the fractional quantum Hall effect. Phys. Rev. Lett. 63, 199–202 (1989)

Jain, J.K.: Theory of the fractional quantum Hall effect. Phys. Rev. B 41, 7653–7665 (1990)

Kung, J.P.S., Rota, G. -C.: The invariant theory of binary forms. Bull. Amer. Math. Soc. 10, 27–85 (1984)

Laughlin, R.B.: Anomalous quantum Hall effect: An incompressible quantum fluid with fractionally charged excitations. Phys. Rev. Lett. 50, 1395–1398 (1983)

Mulay, S.B., Quinn, J.J., Shattuck, M.A.: Correlation diagrams: an intuitive approach to correlations in quantum Hall systems. J. Phys.: Conf. Ser. 702, 1–10 (2016)

Quinn, J.J., Wójs, A., Yi, K. -S., Simion, G.: The hierarchy of incompressible fractional quantum Hall states. Phys. Rep. 481(3–4), 29–81 (2009)

Zariski, O., Samuel, P.: Commutative Algebra, vol. I and II. Springer, New York (1976). Graduate Texts in Mathematics