WIAS Preprint No. 1642, (2011)

Fermionic and bosonic Laughlin state on thick cylinders


  • Jansen, Sabine

2010 Mathematics Subject Classification

  • 81V70 81R40


  • quantum many-body theory, symmetry breaking, quasi-state decomposition, fractional quantum Hall effect, Coulomb systems, jellium, powers of Vandermonde determinants


We investigate a many-body wave function for particles on a cylinder known as Laughlin's function. It is the power of a Vandermonde determinant times a Gaussian. Our main result is: in a many-particle limit, at fixed radius, all correlation functions have a unique limit, and the limit state has a non-trivial period in the axial direction. The result holds regardless how large the radius is, for fermions as well as bosons. In addition, we explain how the algebraic structure used in proofs relates to a ground state perturbation series and to quasi-state decompositions, and we show that the monomer-dimer function introduced in an earlier work is an exact, zero energy, ground state of a suitable finite range Hamiltonian; this is interesting because of formal analogies with some quantum spin chains.

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