The lowest Landau level is the lowest-energy eigenspace of a charged particle's kinetic Hamiltonian in a magnetic field. On a round
sphere with integer flux 
, its one-particle space 
is the spin-
representation of SU(2)
and has dimension 
. It can be realized as homogeneous
polynomials of total degree 
in two spinor coordinates. Projecting an interaction onto
this space gives a finite-dimensional many-body Hamiltonian.
The fermionic 
-particle
space is 
.
The Laughlin spectral-gap conjecture
concerns a specific pair-projector interaction on this space at 
.
Lowest Landau Level
See also
Fock Space, Homogeneous Polynomial, Laughlin Spectral-Gap ConjectureExplore with Wolfram|Alpha
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.Cite this as:
Weisstein, Eric W. "Lowest Landau Level." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/LowestLandauLevel.html