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Laughlin Spectral-Gap Conjecture

The Laughlin spectral-gap conjecture asks for a size-independent positive gap above the Laughlin ground state of its parent interaction. In the spherical fermionic filling-1/3 formulation, let U_Q be the lowest Landau level at flux Q and define

H_(N,Q)=sum_(i<j)P_(ij)^((1)),

on ^ ^(N)U_Q, where P_(ij)^((1)) projects the pair onto total spin Q-1, or relative angular momentum one. Each unordered pair has coefficient one. At Q=3(N-1) the zero-energy ground vector is proportional to product_(i<j)(u_iv_j-u_jv_i)^3 in spinor coordinates.

See also

Fock Space, Ground State, Lowest Landau Level, Spectral Gap

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References

Greiter, M. Mapping of Parent Hamiltonians: From Abelian and non-Abelian Quantum Hall States to Exact Models of Critical Spin Chains. Berlin, Germany: Springer, 2011. https://doi.org/10.1007/978-3-642-24384-4.Rougerie, N. "On the Laughlin Function and Its Perturbations." Sém. Laurent Schwartz EDP Appl. 2, 2018. https://doi.org/10.5802/slsedp.131.

Cite this as:

Weisstein, Eric W. "Laughlin Spectral-Gap Conjecture." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/LaughlinSpectral-GapConjecture.html

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