Fermionic and bosonic Laughlin state on thick cylinders

Details Fermionic and bosonic Laughlin state on thick cylinders Fermionic and bosonic Laughlin state on thick cylinders

2011-09-19

arxiv.org/abs/1109.4022v1

Physics

Mathematical Physics

49 pages

Scientific paper

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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